{"title":"Analytical Solutions of Kortweg-de Vries(KdV) Equation","authors":"Foad Saadi, M. Jalali Azizpour, S.A. Zahedi","volume":45,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":1252,"pagesEnd":1257,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14562","abstract":"The objective of this paper is to present a\r\ncomparative study of Homotopy Perturbation Method (HPM),\r\nVariational Iteration Method (VIM) and Homotopy Analysis\r\nMethod (HAM) for the semi analytical solution of Kortweg-de\r\nVries (KdV) type equation called KdV. The study have been\r\nhighlighted the efficiency and capability of aforementioned methods\r\nin solving these nonlinear problems which has been arisen from a\r\nnumber of important physical phenomenon.","references":"[1] D.J. Korteweg, G. de Vries, On the change of form of long waves\r\nadvancing in a rectangular canal, and on a new type of long stationary\r\nwave, Philos. Mag. Vol.39, 1895, pp. 422-443.\r\n[2] Luwai Wazzan, A modified tanh-coth method for solving the KdV and\r\nthe KdV-Burgers equations, Journal of Communication in nonlinear\r\nscience and numerical simulation, (2007)\r\n[3] A.J. Khattak, Siraj-ul-Islam, A comparative study of numerical solutions\r\nof a class of KdV equation , Journal of Computnational Applied\r\nMathematical, Vol. 199, 2008 , pp.425-434.\r\n[4] T. Ozis, S. Ozer S, A simple similarity-transformation-iterative scheme\r\napplied to Korteweg-de Vries equation, Journal of Applied\r\nMathematical Compution, Vol. 173, 2006, pp.19-32.\r\n[5] Abdul-Majid Wazwaz, The variational iteration method for rational\r\nsolutions for KdV, K(2,2) Burgers and cubic Boussinesq equations,\r\nJournal of Computional Applied Mathematical, Article, (2006)\r\n[6] P. Rosenau, J. M. Hyman, Compactons Solitons with finite\r\nwavelengths, Physics. Review Letter. Vol.70, No.5, 1993, pp. 564 -567.\r\n[7] M.A. Abdou, A.A. Soliman, Variational iteration method for solving\r\nBurger's and coupled Burger's equation, Journal in Computensional\r\nApplied Mathematical, Vol.181, 2005, pp.245-251\r\n[8] E.M. Aboulvafa, M.A. Abdou, A.A. Mahmoud, The solution of nonlinear\r\ncoagulation problem with mass loss, Chaos Solitons And Fractals\r\nVol.29, 2006, pp.313-330\r\n[9] J.H. He, A new approach to nonlinear partial differential equations,\r\nComm. Nonlinear Science and Numereical Simulation, Vol.2, No.4,\r\n1997, pp.203-205.\r\n[10] S.J. Liao, The proposed homotopy analysis technique for the solution of\r\nnonlinear problems, PhD thesis Shanghai Jiao Tong University, 1992\r\n[11] N. Tolou. I. Khatami. B. Jafari. D.D. Ganji. Analytical Solution of\r\nNonlinear Vibrating Systems. American journal of applied Sciences,\r\nVol.5, No.9, 2008, pp.1219-1224.\r\n[12] M.J. Ablowitz, P.A. Clarkson, Solitions, Nonlinear Evolution Equations\r\nand Inverse Scattering, Cambridge University Press, 1991\r\n[13] A. Coely, (Eds.), Backlund and Darboux Transformations, American\r\nMathematical Society, Providence, Rhode Island, 2001\r\n[14] M. Wadati, H. Sanuki, K. Konno, Relationships among inverse method,\r\nbacklund transformation and an infinite number of conservation laws,\r\nProg. Theoret. Phys. Vol.53, 1975, pp.419-436\r\n[15] C.S. Gardner, J.M. Green, M.D. Kruskal, R.M. Miura, Method for\r\nsolving the Korteweg-deVries equation, Phys. Rev. Lett. Vol.19, 1967,\r\npp.1095-1097\r\n[16] J.H. He, Homotopy perturbation method for bifurcation of nonlinear\r\nproblems\", Int. J. Non-linear Sci. Num. Sim., 6(2): 207-208 (2005)\r\n[17] S.J. Liao, Beyond Perturbation: Introduction to the homotopy Analysis\r\nMethod, Chapman & Hall\/CRC press, Boca Raton, (2003)\r\n[18] S. Abbasbandy, The application of homotopy analysis method to\r\nnonlinear equations arising in heat transfer, Phys. Lett. A","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 45, 2010"}