Document Zbl 1364.37146

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The formula obtained allows one to get, as a particular case, the $N$-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6730324">Cited in <strong>24</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><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%3A37M05" title="MSC2020">37M05</a> </td> <td class="space"> Simulation of dynamical systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35C08" title="MSC2020">35C08</a> </td> <td class="space"> Soliton solutions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asoliton+solutions">soliton solutions</a>; <a href="/?q=ut%3Avortex+filaments">vortex filaments</a>; <a href="/?q=ut%3Ainverse+scattering+transform">inverse scattering transform</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 1364.37146" data-ciurl="/ci/06730324" data-biburl="/bibtex/06730324.bib" data-amsurl="/amsrefs/06730324.bib" data-xmlurl="/xml/06730324.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06730324.pdf" title="Zbl 1364.37146 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.physd.2015.09.009" aria-label="DOI for “Exact solutions of the Hirota equation and vortex filaments motion”" title="10.1016/j.physd.2015.09.009">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/10281/97928" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Hirota, R., Exact envelope-soliton solutions of a nonlinear wave equation, J. 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