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J. Phys., Taipei</a> <a href="/?q=in%3A512361" title="Articles in this Issue">68, 605-617 (2020)</a>. </div> <div class="abstract">Summary: This work deals with the constitute of numerical solutions of the generalized Korteweg-de Vries (GKdV) equation with Petrov-Galerkin finite element approach utilising a cubic B-spline function as the trial function and a quadratic function as the test function. Accurateness and effectiveness of the submitted methods are shown by employing propagation of single solitary wave. The \(L_2\), \(L_\infty\) error norms and \(I_1\), \(I_2\) and \(I_3\) invariants are used to validate the applicability and durability of our numerical algorithm. Implementing the Von-Neumann theory, it is manifested that the suggested method is marginally stable. Furthermore, supernonlinear traveling wave solution of the GKdV equation is presented using phase plots. It is seen that the GKdV equation supports superperiodic traveling wave solution only and it is significantly affected by velocity and nonlinear parameters. Also, considering a superficial periodic forcing multistability of traveling waves of perturbed GKdV equation is presented. It is found that the perturbed GKdV equation supports coexisting chaotic and various quasiperiodic features with same parametric values at different initial conditions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7848626">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M10" title="MSC2020">76M10</a> </td> <td class="space"> Finite element methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M60" title="MSC2020">65M60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D07" title="MSC2020">65D07</a> </td> <td class="space"> Numerical computation using splines </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76B25" title="MSC2020">76B25</a> </td> <td class="space"> Solitary waves for incompressible inviscid fluids </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afinite+element+method">finite element method</a>; <a href="/?q=ut%3APetrov-Galerkin">Petrov-Galerkin</a>; <a href="/?q=ut%3Acubic+B-spline">cubic B-spline</a>; <a href="/?q=ut%3Asoliton">soliton</a>; <a href="/?q=ut%3Asupernonlinear+wave">supernonlinear wave</a>; <a href="/?q=ut%3Acoexisting+orbits">coexisting orbits</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1550.76155" data-ciurl="/ci/07848626" data-biburl="/bibtex/07848626.bib" data-amsurl="/amsrefs/07848626.bib" data-xmlurl="/xml/07848626.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07848626.pdf" title="Zbl 1550.76155 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cjph.2020.10.010" aria-label="DOI for “A novel implementation of Petrov-Galerkin method to shallow water solitary wave pattern and superperiodic traveling wave and its multistability: generalized Korteweg-de Vries equation”" title="10.1016/j.cjph.2020.10.010">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abdou, M. 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