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equation</title> <meta name="description" content="Search results for: Schrodinger equation"> <meta name="keywords" content="Schrodinger equation"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Schrodinger equation"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1097</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Schrodinger equation</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1097</span> Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Emad%20K.%20Jaradat">Emad K. Jaradat</a>, <a href="https://publications.waset.org/search?q=Ala%E2%80%99a%20Al-Faqih"> Ala’a Al-Faqih</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Non-linear%20Schrodinger%20equation" title="Non-linear Schrodinger equation">Non-linear Schrodinger equation</a>, <a href="https://publications.waset.org/search?q=Elzaki%20decomposition%20method" title=" Elzaki decomposition method"> Elzaki decomposition method</a>, <a href="https://publications.waset.org/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a>, <a href="https://publications.waset.org/search?q=one%20and%20two-%20dimensional%20Schrodinger%20equation." title=" one and two- dimensional Schrodinger equation. "> one and two- dimensional Schrodinger equation. </a> </p> <a href="https://publications.waset.org/10010018/approximate-solution-to-non-linear-schrodinger-equation-with-harmonic-oscillator-by-elzaki-decomposition-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010018/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010018/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010018/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010018/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010018/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010018/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010018/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010018/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010018/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010018/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010018.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">904</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1096</span> An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=%C4%B0nci%20M.%20Erhan">İnci M. Erhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bessel%20functions" title="Bessel functions">Bessel functions</a>, <a href="https://publications.waset.org/search?q=Eigenfunction%20expansion" title=" Eigenfunction expansion"> Eigenfunction expansion</a>, <a href="https://publications.waset.org/search?q=Quantum%20billiard" title=" Quantum billiard"> Quantum billiard</a>, <a href="https://publications.waset.org/search?q=Schr%C3%B6dinger%20equation" title=" Schrödinger equation"> Schrödinger equation</a>, <a href="https://publications.waset.org/search?q=Spherical%20harmonics" title=" Spherical harmonics"> Spherical harmonics</a> </p> <a href="https://publications.waset.org/1846/an-expansion-method-for-schrodinger-equation-of-quantum-billiards-with-arbitrary-shapes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1846/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1846/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1846/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1846/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1846/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1846/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1846/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1846/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1846/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1846/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1846.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">5215</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1095</span> Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=I.%20Otete">I. Otete</a>, <a href="https://publications.waset.org/search?q=A.%20I.%20Ejere"> A. I. Ejere</a>, <a href="https://publications.waset.org/search?q=I.%20S.%20Okunzuwa"> I. S. Okunzuwa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Schr%C3%B6dinger%27s%20equation" title="Schrödinger's equation">Schrödinger's equation</a>, <a href="https://publications.waset.org/search?q=bound%20state" title=" bound state"> bound state</a>, <a href="https://publications.waset.org/search?q=Hulthen-Yukawa%20potential" title=" Hulthen-Yukawa potential"> Hulthen-Yukawa potential</a>, <a href="https://publications.waset.org/search?q=Nikiforov-Uvarov" title=" Nikiforov-Uvarov"> Nikiforov-Uvarov</a>, <a href="https://publications.waset.org/search?q=D-dimensions" title=" D-dimensions"> D-dimensions</a> </p> <a href="https://publications.waset.org/10012347/bound-state-solutions-of-the-schrodinger-equation-for-hulthen-yukawa-potential-in-d-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10012347/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10012347/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10012347/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10012347/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10012347/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10012347/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10012347/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10012347/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10012347/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10012347/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10012347.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">453</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1094</span> Photon Localization inside a Waveguide Modeled by Uncertainty Principle</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Shilpa%20N.%20Kulkarni">Shilpa N. Kulkarni</a>, <a href="https://publications.waset.org/search?q=Sujata%20R.%20Patrikar"> Sujata R. Patrikar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present work, an attempt is made to understand electromagnetic field confinement in a subwavelength waveguide structure using concepts of quantum mechanics. Evanescent field in the waveguide is looked as inability of the photon to get confined in the waveguide core and uncertainty of position is assigned to it. The momentum uncertainty is calculated from position uncertainty. Schrödinger wave equation for the photon is written by incorporating position-momentum uncertainty. The equation is solved and field distribution in the waveguide is obtained. The field distribution and power confinement is compared with conventional waveguide theory. They were found in good agreement with each other. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=photon%20localization%20in%20waveguide" title="photon localization in waveguide">photon localization in waveguide</a>, <a href="https://publications.waset.org/search?q=photon%20tunneling" title=" photon tunneling"> photon tunneling</a>, <a href="https://publications.waset.org/search?q=quantum%20confinement%20of%20light" title=" quantum confinement of light"> quantum confinement of light</a>, <a href="https://publications.waset.org/search?q=Schr%C3%B6dinger%20wave%20equation" title=" Schrödinger wave equation"> Schrödinger wave equation</a>, <a href="https://publications.waset.org/search?q=uncertainty%20principle." title=" uncertainty principle."> uncertainty principle.</a> </p> <a href="https://publications.waset.org/2418/photon-localization-inside-a-waveguide-modeled-by-uncertainty-principle" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2418/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2418/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2418/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2418/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2418/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2418/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2418/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2418/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2418/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2418/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2418.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2918</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1093</span> Calculation of Wave Function at the Origin (WFO) for Heavy Mesons by Numerical Solving of the Schrodinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Momeni%20Feyli">M. Momeni Feyli</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many recent high energy physics calculations involving charm and beauty invoke wave function at the origin (WFO) for the meson bound state. Uncertainties of charm and beauty quark masses and different models for potentials governing these bound states require a simple numerical algorithm for evaluation of the WFO's for these bound states. We present a simple algorithm for this propose which provides WFO's with high precision compared with similar ones already obtained in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Mesons" title="Mesons">Mesons</a>, <a href="https://publications.waset.org/search?q=Bound%20states" title=" Bound states"> Bound states</a>, <a href="https://publications.waset.org/search?q=Schrodinger%20equation" title=" Schrodinger equation"> Schrodinger equation</a>, <a href="https://publications.waset.org/search?q=Nonrelativistic%0Aquark%20model." title=" Nonrelativistic quark model."> Nonrelativistic quark model.</a> </p> <a href="https://publications.waset.org/465/calculation-of-wave-function-at-the-origin-wfo-for-heavy-mesons-by-numerical-solving-of-the-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/465/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/465/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/465/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/465/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/465/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/465/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/465/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/465/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/465/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/465/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/465.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1503</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1092</span> CO-OFDM DSP Channel Estimation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Pranav%20Ravikumar">Pranav Ravikumar</a>, <a href="https://publications.waset.org/search?q=Arunabha%20Bera"> Arunabha Bera</a>, <a href="https://publications.waset.org/search?q=Vijay%20K.%20Mehra"> Vijay K. Mehra</a>, <a href="https://publications.waset.org/search?q=Anand%20Kumar"> Anand Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Modulation" title="Modulation">Modulation</a>, <a href="https://publications.waset.org/search?q=Non%20Linear%20Schrodinger%20Equation" title=" Non Linear Schrodinger Equation"> Non Linear Schrodinger Equation</a>, <a href="https://publications.waset.org/search?q=Optical%20fiber" title=" Optical fiber"> Optical fiber</a>, <a href="https://publications.waset.org/search?q=Split%20Step%20Fourier%20Method." title=" Split Step Fourier Method."> Split Step Fourier Method.</a> </p> <a href="https://publications.waset.org/10705/co-ofdm-dsp-channel-estimation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10705/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10705/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10705/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10705/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10705/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10705/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10705/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10705/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10705/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10705/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10705.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2787</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1091</span> Impact of the Existence of One-Way Functionson the Conceptual Difficulties of Quantum Measurements</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Arkady%20Bolotin">Arkady Bolotin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way function. The assumption implies that at the macroscopic level the Schrödinger equation becomes unfeasible to compute. This unfeasibility plays a role of limit of the validity of the linear Schrödinger equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=One-way%20functions" title="One-way functions">One-way functions</a>, <a href="https://publications.waset.org/search?q=P%20versus%20NP%20problem" title=" P versus NP problem"> P versus NP problem</a>, <a href="https://publications.waset.org/search?q=quantummeasurements." title=" quantummeasurements."> quantummeasurements.</a> </p> <a href="https://publications.waset.org/2946/impact-of-the-existence-of-one-way-functionson-the-conceptual-difficulties-of-quantum-measurements" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2946/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2946/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2946/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2946/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2946/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2946/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2946/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2946/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2946/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2946/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2946.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1308</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1090</span> Instability of Soliton Solutions to the Schamel-nonlinear Schrödinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sarun%20Phibanchon">Sarun Phibanchon</a>, <a href="https://publications.waset.org/search?q=Michael%20A.%20Allen"> Michael A. Allen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr┬¿odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Soliton" title="Soliton">Soliton</a>, <a href="https://publications.waset.org/search?q=instability" title=" instability"> instability</a>, <a href="https://publications.waset.org/search?q=variational%20method" title=" variational method"> variational method</a>, <a href="https://publications.waset.org/search?q=spectral%20method." title=" spectral method."> spectral method.</a> </p> <a href="https://publications.waset.org/10680/instability-of-soliton-solutions-to-the-schamel-nonlinear-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10680/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10680/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10680/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10680/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10680/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10680/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10680/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10680/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10680/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10680/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10680.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3700</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1089</span> Numerical Study of Some Coupled PDEs by using Differential Transformation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Reza%20Abazari">Reza Abazari</a>, <a href="https://publications.waset.org/search?q=Rasool%20Abazari"> Rasool Abazari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Coupled%20Korteweg-de%20Vries%28KdV%29%20equation" title="Coupled Korteweg-de Vries(KdV) equation">Coupled Korteweg-de Vries(KdV) equation</a>, <a href="https://publications.waset.org/search?q=Coupled%20Burgers%20equation" title=" Coupled Burgers equation"> Coupled Burgers equation</a>, <a href="https://publications.waset.org/search?q=Coupled%20Schr%C3%B6dinger%20equation" title=" Coupled Schrödinger equation"> Coupled Schrödinger equation</a>, <a href="https://publications.waset.org/search?q=differential%20transformation%20method." title=" differential transformation method."> differential transformation method.</a> </p> <a href="https://publications.waset.org/9113/numerical-study-of-some-coupled-pdes-by-using-differential-transformation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9113/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9113/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9113/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9113/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9113/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9113/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9113/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9113/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9113/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9113/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9113.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3001</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1088</span> Schrödinger Equation with Position-Dependent Mass: Staggered Mass Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=J.%20J.%20Pe%C3%B1a">J. J. Peña</a>, <a href="https://publications.waset.org/search?q=J.%20Morales"> J. Morales</a>, <a href="https://publications.waset.org/search?q=J.%20Garc%C3%ADa-Ravelo"> J. García-Ravelo</a>, <a href="https://publications.waset.org/search?q=L.%20Arcos-D%C3%ADaz"> L. Arcos-Díaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Free%20particle" title="Free particle">Free particle</a>, <a href="https://publications.waset.org/search?q=point%20canonical%20transformation%20method" title=" point canonical transformation method"> point canonical transformation method</a>, <a href="https://publications.waset.org/search?q=position-dependent%20mass" title=" position-dependent mass"> position-dependent mass</a>, <a href="https://publications.waset.org/search?q=staggered%20mass%20distribution." title=" staggered mass distribution."> staggered mass distribution.</a> </p> <a href="https://publications.waset.org/10007521/schrodinger-equation-with-position-dependent-mass-staggered-mass-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10007521/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10007521/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10007521/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10007521/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10007521/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10007521/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10007521/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10007521/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10007521/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10007521/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10007521.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1572</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1087</span> Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tomoaki%20Hashimoto">Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Optimal%20control" title="Optimal control">Optimal control</a>, <a href="https://publications.waset.org/search?q=stochastic%20systems" title=" stochastic systems"> stochastic systems</a>, <a href="https://publications.waset.org/search?q=quantum%20systems" title=" quantum systems"> quantum systems</a>, <a href="https://publications.waset.org/search?q=stabilization." title=" stabilization."> stabilization.</a> </p> <a href="https://publications.waset.org/10006052/stability-of-stochastic-model-predictive-control-for-schrodinger-equation-with-finite-approximation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006052/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006052/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006052/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006052/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006052/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006052/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006052/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006052/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006052/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006052/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006052.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2356</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1086</span> Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anupma%20Bansal">Anupma Bansal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Klein-Gordon-Sch%C3%B6dinger%20Equation" title="Klein-Gordon-Schödinger Equation">Klein-Gordon-Schödinger Equation</a>, <a href="https://publications.waset.org/search?q=Lie%20Classical%20Method" title=" Lie Classical Method"> Lie Classical Method</a>, <a href="https://publications.waset.org/search?q=Exact%20Solutions" title=" Exact Solutions"> Exact Solutions</a> </p> <a href="https://publications.waset.org/16742/constructing-distinct-kinds-of-solutions-for-the-time-dependent-coefficients-coupled-klein-gordon-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16742/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16742/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16742/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16742/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16742/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16742/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16742/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16742/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16742/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16742/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16742.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">4530</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1085</span> Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Saravi">M. Saravi</a>, <a href="https://publications.waset.org/search?q=F.%20Ashrafi"> F. Ashrafi</a>, <a href="https://publications.waset.org/search?q=S.R.%20Mirrajei"> S.R. Mirrajei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title="Chebyshev polynomials">Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=Clenshaw%20method" title=" Clenshaw method"> Clenshaw method</a>, <a href="https://publications.waset.org/search?q=ODEs" title=" ODEs"> ODEs</a>, <a href="https://publications.waset.org/search?q=Spectral%20methods" title=" Spectral methods"> Spectral methods</a> </p> <a href="https://publications.waset.org/10826/numerical-solution-of-linear-ordinary-differential-equations-in-quantum-chemistry-by-clenshaw-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10826/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10826/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10826/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10826/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10826/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10826/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10826/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10826/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10826/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10826/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10826.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1420</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1084</span> On the Integer Solutions of the Pell Equation x2 - dy2 = 2t</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer"> Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=Diophantine%20equation." title=" Diophantine equation."> Diophantine equation.</a> </p> <a href="https://publications.waset.org/423/on-the-integer-solutions-of-the-pell-equation-x2-dy2-2t" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/423/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/423/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/423/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/423/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/423/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/423/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/423/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/423/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/423/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/423/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/423.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2387</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1083</span> The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Armend%20Sh.%20Shabani">Armend Sh. Shabani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%27s%20equation" title="Pell's equation">Pell's equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%27s%20equation." title=" solutions of Pell's equation."> solutions of Pell's equation.</a> </p> <a href="https://publications.waset.org/14954/the-proof-of-two-conjectures-related-to-pell-s-equation-x2-dy2-4" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14954/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14954/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14954/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14954/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14954/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14954/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14954/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14954/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14954/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14954/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14954.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1238</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1082</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Riccati%20Equation" title="Riccati Equation">Riccati Equation</a>, <a href="https://publications.waset.org/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20differential%20equation" title=" nonlinear differential equation"> nonlinear differential equation</a>, <a href="https://publications.waset.org/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/search?q=proper%20solution." title=" proper solution."> proper solution.</a> </p> <a href="https://publications.waset.org/10006683/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006683/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006683/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006683/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006683/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006683/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006683/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006683/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006683/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006683/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006683/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006683.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2024</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1081</span> The Pell Equation x2 − Py2 = Q</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Canan%20Kocap%C4%B1nar"> Canan Kocapınar</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%20equation." title=" solutions of Pell equation."> solutions of Pell equation.</a> </p> <a href="https://publications.waset.org/7822/the-pell-equation-x2-py2-q" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7822/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7822/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7822/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7822/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7822/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7822/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7822/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7822/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7822/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7822/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7822.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2106</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1080</span> The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Diophantine%20equation" title="Diophantine equation">Diophantine equation</a>, <a href="https://publications.waset.org/search?q=Pell%20equation" title=" Pell equation"> Pell equation</a>, <a href="https://publications.waset.org/search?q=quadratic%20form." title=" quadratic form."> quadratic form.</a> </p> <a href="https://publications.waset.org/6133/the-diophantine-equation-y2-2yx-3-0-and-corresponding-curves-over-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6133/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6133/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6133/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6133/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6133/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6133/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6133/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6133/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6133/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6133/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1266</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1079</span> Modulational Instability of Electron Plasma Waves in Finite Temperature Quantum Plasma</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Swarniv%20Chandra"> Swarniv Chandra</a>, <a href="https://publications.waset.org/search?q=Basudev%20Ghosh"> Basudev Ghosh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Amplitude%20Modulation" title="Amplitude Modulation">Amplitude Modulation</a>, <a href="https://publications.waset.org/search?q=Electron%20Plasma%20Waves" title=" Electron Plasma Waves"> Electron Plasma Waves</a>, <a href="https://publications.waset.org/search?q=Finite%20Temperature%20Model" title=" Finite Temperature Model"> Finite Temperature Model</a>, <a href="https://publications.waset.org/search?q=Modulational%20Instability" title=" Modulational Instability"> Modulational Instability</a>, <a href="https://publications.waset.org/search?q=Quantum%0D%0APlasma." title=" Quantum Plasma."> Quantum Plasma.</a> </p> <a href="https://publications.waset.org/11089/modulational-instability-of-electron-plasma-waves-in-finite-temperature-quantum-plasma" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11089/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11089/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11089/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11089/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11089/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11089/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11089/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11089/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11089/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11089/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11089.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1693</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1078</span> Solution of The KdV Equation with Asymptotic Degeneracy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tapas%20Kumar%20Sinha">Tapas Kumar Sinha</a>, <a href="https://publications.waset.org/search?q=Joseph%20Mathew"> Joseph Mathew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=KdV%20equation" title="KdV equation">KdV equation</a>, <a href="https://publications.waset.org/search?q=Asymptotic%20Degeneracy" title=" Asymptotic Degeneracy"> Asymptotic Degeneracy</a>, <a href="https://publications.waset.org/search?q=Solitons" title=" Solitons"> Solitons</a>, <a href="https://publications.waset.org/search?q=Inverse%20Scattering" title=" Inverse Scattering"> Inverse Scattering</a> </p> <a href="https://publications.waset.org/1871/solution-of-the-kdv-equation-with-asymptotic-degeneracy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1871/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1871/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1871/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1871/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1871/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1871/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1871/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1871/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1871/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1871/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1871.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1620</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1077</span> Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Said%20Laachir">Said Laachir</a>, <a href="https://publications.waset.org/search?q=Aziz%20Laaribi"> Aziz Laaribi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Helmholtz%20equation" title="Helmholtz equation">Helmholtz equation</a>, <a href="https://publications.waset.org/search?q=Nikiforov-Uvarov%20method" title=" Nikiforov-Uvarov method"> Nikiforov-Uvarov method</a>, <a href="https://publications.waset.org/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/search?q=eigenfunctions." title=" eigenfunctions."> eigenfunctions.</a> </p> <a href="https://publications.waset.org/9996665/exact-solutions-of-the-helmholtz-equation-via-the-nikiforov-uvarov-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996665/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996665/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996665/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996665/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996665/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996665/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996665/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996665/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996665/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996665/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996665.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3003</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1076</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nara%20Guimar%C3%A3es">Nara Guimarães</a>, <a href="https://publications.waset.org/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouvêa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/search?q=phase%0D%0Aseparation." title=" phase separation."> phase separation.</a> </p> <a href="https://publications.waset.org/10000644/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000644/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000644/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000644/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000644/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000644/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000644/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000644/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000644/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000644/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000644/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000644.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2053</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1075</span> Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hidetoshi%20Konno"> Hidetoshi Konno</a>, <a href="https://publications.waset.org/search?q=Akio%20Suzuki"> Akio Suzuki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Transient%20population%20dynamics" title=" Transient population dynamics"> Transient population dynamics</a>, <a href="https://publications.waset.org/search?q=Phase%20singularity" title=" Phase singularity"> Phase singularity</a>, <a href="https://publications.waset.org/search?q=Birth-death%20process" title=" Birth-death process"> Birth-death process</a>, <a href="https://publications.waset.org/search?q=Non-stationary%20Master%20equation" title=" Non-stationary Master equation"> Non-stationary Master equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20Langevin%20equation" title=" nonlinear Langevin equation"> nonlinear Langevin equation</a>, <a href="https://publications.waset.org/search?q=generalized%20Logistic%20equation." title=" generalized Logistic equation."> generalized Logistic equation.</a> </p> <a href="https://publications.waset.org/16095/transient-population-dynamics-of-phase-singularities-in-2d-beeler-reuter-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16095/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16095/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16095/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16095/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16095/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16095/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16095/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16095/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16095/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16095/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16095.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1593</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1074</span> Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nisha%20Goyal">Nisha Goyal</a>, <a href="https://publications.waset.org/search?q=R.K.%20Gupta"> R.K. Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Sawada-Kotera-Kadomtsev-Petviashivili%20equation" title="Sawada-Kotera-Kadomtsev-Petviashivili equation">Sawada-Kotera-Kadomtsev-Petviashivili equation</a>, <a href="https://publications.waset.org/search?q=Bogoyavlensky-Konoplechenko%20equation" title=" Bogoyavlensky-Konoplechenko equation"> Bogoyavlensky-Konoplechenko equation</a>, <a href="https://publications.waset.org/search?q=" title=" "> </a> </p> <a href="https://publications.waset.org/15030/traveling-wave-solutions-for-the-sawada-kotera-kadomtsev-petviashivili-equation-and-the-bogoyavlensky-konoplechenko-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15030/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15030/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15030/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15030/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15030/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15030/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15030/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15030/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15030/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15030/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15030.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1617</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1073</span> Stability of Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Lane-Emden%20equation" title=" Lane-Emden equation"> Lane-Emden equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%20integral%20equation." title=" Volterra integral equation."> Volterra integral equation.</a> </p> <a href="https://publications.waset.org/16803/stability-of-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16803/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16803/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16803/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16803/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16803/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16803/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16803/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16803/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16803/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16803/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16803.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3718</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1072</span> Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anjali%20Verma">Anjali Verma</a>, <a href="https://publications.waset.org/search?q=Ram%20Jiwari"> Ram Jiwari</a>, <a href="https://publications.waset.org/search?q=Jitender%20Kumar"> Jitender Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20wave%20equation" title="Shallow water wave equation">Shallow water wave equation</a>, <a href="https://publications.waset.org/search?q=Exact%20solutions" title=" Exact solutions"> Exact solutions</a>, <a href="https://publications.waset.org/search?q=%02%28G%27%2FG%29%20expansion%20method." title=" (G'/G) expansion method."> (G'/G) expansion method.</a> </p> <a href="https://publications.waset.org/16740/traveling-wave-solutions-for-shallow-water-wave-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16740/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16740/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16740/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16740/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16740/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16740/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16740/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16740/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16740/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16740/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16740.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1839</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1071</span> Existence of Iterative Cauchy Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Cauchy%20equation" title=" Cauchy equation"> Cauchy equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%0D%0Aintegral%20equation" title=" Volterra integral equation"> Volterra integral equation</a>, <a href="https://publications.waset.org/search?q=non-expansive%20mapping" title=" non-expansive mapping"> non-expansive mapping</a>, <a href="https://publications.waset.org/search?q=iterative%20differential%20equation." title=" iterative differential equation."> iterative differential equation.</a> </p> <a href="https://publications.waset.org/17037/existence-of-iterative-cauchy-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17037/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17037/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17037/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17037/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17037/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17037/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17037/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17037/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17037/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17037/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17037.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2684</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1070</span> FWM Wavelength Conversion Analysis in a 3-Integrated Portion SOA and DFB Laser using Coupled Wave Approach and FD-BPM Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20K.%20Moazzam">M. K. Moazzam</a>, <a href="https://publications.waset.org/search?q=A.%20Salmanpour"> A. Salmanpour</a>, <a href="https://publications.waset.org/search?q=M.%20Nirouei"> M. Nirouei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we have numerically analyzed terahertzrange wavelength conversion using nondegenerate four wave mixing (NDFWM) in a SOA integrated DFB laser (experiments reported both in MIT electronics and Fujitsu research laboratories). For analyzing semiconductor optical amplifier (SOA), we use finitedifference beam propagation method (FDBPM) based on modified nonlinear SchrÖdinger equation and for distributed feedback (DFB) laser we use coupled wave approach. We investigated wavelength conversion up to 4THz probe-pump detuning with conversion efficiency -5dB in 1THz probe-pump detuning for a SOA integrated quantum-well <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=distributed%20feedback%20laser" title="distributed feedback laser">distributed feedback laser</a>, <a href="https://publications.waset.org/search?q=nondegenerate%20fourwave%20mixing" title=" nondegenerate fourwave mixing"> nondegenerate fourwave mixing</a>, <a href="https://publications.waset.org/search?q=semiconductor%20optical%20amplifier" title=" semiconductor optical amplifier"> semiconductor optical amplifier</a>, <a href="https://publications.waset.org/search?q=wavelengthconversion" title=" wavelengthconversion"> wavelengthconversion</a> </p> <a href="https://publications.waset.org/14976/fwm-wavelength-conversion-analysis-in-a-3-integrated-portion-soa-and-dfb-laser-using-coupled-wave-approach-and-fd-bpm-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14976/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14976/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14976/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14976/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14976/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14976/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14976/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14976/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14976/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14976/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14976.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1506</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1069</span> Ginzburg-Landau Model for Curved Two-Phase Shallow Mixing Layers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Irina%20Eglite">Irina Eglite</a>, <a href="https://publications.waset.org/search?q=Andrei%20A.%20Kolyshkin"> Andrei A. Kolyshkin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20equations" title="Shallow water equations">Shallow water equations</a>, <a href="https://publications.waset.org/search?q=mixing%20layer" title=" mixing layer"> mixing layer</a>, <a href="https://publications.waset.org/search?q=weakly%0Anonlinear%20analysis" title=" weakly nonlinear analysis"> weakly nonlinear analysis</a>, <a href="https://publications.waset.org/search?q=Ginzburg-Landau%20equation" title=" Ginzburg-Landau equation"> Ginzburg-Landau equation</a> </p> <a href="https://publications.waset.org/14646/ginzburg-landau-model-for-curved-two-phase-shallow-mixing-layers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14646/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14646/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14646/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14646/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14646/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14646/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14646/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14646/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14646/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14646/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14646.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1419</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1068</span> Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mohammad%20Taghi%20Darvishi">Mohammad Taghi Darvishi</a>, <a href="https://publications.waset.org/search?q=Maliheh%20Najafi"> Maliheh Najafi</a>, <a href="https://publications.waset.org/search?q=Mohammad%20Najafi"> Mohammad Najafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Exact%20solution" title="Exact solution">Exact solution</a>, <a href="https://publications.waset.org/search?q=The%20%283%2B1%29-dimensional%20breaking%20soliton%20equation" title=" The (3+1)-dimensional breaking soliton equation"> The (3+1)-dimensional breaking soliton equation</a>, <a href="https://publications.waset.org/search?q=%28%20G%20G%20%29-expansion%20method" title=" ( G G )-expansion method"> ( G G )-expansion method</a>, <a href="https://publications.waset.org/search?q=Riccati%20equation" title=" Riccati equation"> Riccati equation</a>, <a href="https://publications.waset.org/search?q=Modified%20Fexpansion%20method." title=" Modified Fexpansion method."> Modified Fexpansion method.</a> </p> <a href="https://publications.waset.org/12188/traveling-wave-solutions-for-the-31-dimensional-breaking-soliton-equation-by-gg-expansion-method-and-modified-f-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12188/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12188/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12188/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12188/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12188/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12188/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a 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