Document Zbl 1459.37056

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For the direct scattering problem, the spectral analysis is performed for the equation, from which a Riemann-Hilbert problem is well constructed. For the inverse scattering problem, the Riemann-Hilbert problem corresponding to the reflection-less case is solved. Furthermore, as applications, three types of multi-soliton solutions are found. Finally, some figures are presented to discuss the soliton behaviors of the vmKdV equation.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7341823">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A37K10" title="MSC2020">37K10</a> </td> <td class="space"> Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q53" title="MSC2020">35Q53</a> </td> <td class="space"> KdV equations (Korteweg-de Vries equations) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37K40" title="MSC2020">37K40</a> </td> <td class="space"> Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37K15" title="MSC2020">37K15</a> </td> <td class="space"> Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainverse+scattering+transform">inverse scattering transform</a>; <a href="/?q=ut%3ARiemann-Hilbert+problem">Riemann-Hilbert problem</a>; <a href="/?q=ut%3Amulti-soliton+solutions">multi-soliton solutions</a></div>  <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;">  </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">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1459.37056" data-ciurl="/ci/07341823" data-biburl="/bibtex/07341823.bib" data-amsurl="/amsrefs/07341823.bib" data-xmlurl="/xml/07341823.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07341823.pdf" title="Zbl 1459.37056 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/10.1007/s11071-019-05359-x" aria-label="DOI for “Application of the Riemann-Hilbert method to the vector modified Korteweg-de Vries equation”" title="10.1007/s11071-019-05359-x">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">Wazwaz, Am; 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