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Differ. Equations</a> <a href="/?q=in%3A51523" title="Articles in this Issue">149, No. 2, 248-291 (1998)</a>. </div> <div class="abstract">Summary: The authors study the existence and stability of travelling waves in lattice dynamical systems, in particular, in lattice ordinary differential equations (lattice ODEs) and in coupled map lattices (CMLs). Instead of employing the moving coordinate approach as for partial differential equations they construct a local coordinate system around a traveling wave solution to a lattice ODE, analogous to the local coordinate system around a periodic solution to an ODE. In this coordinate system the lattice ODE becomes a nonautonomous periodic differential equation, and the traveling wave corresponds to a periodic solution to this equation. The authors prove the asymptotic stability with asymptotic phase shift of the traveling wave solution under appropriate spectral conditions. It is shown the existence of traveling waves in CMLs which arise as time-discretizations of lattice ODEs. Finally, these results are applied to the discrete Nagumo equation. \(\copyright\) 1998 Academic Press.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A1216512">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A1216512">Cited in <strong>230</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D30" title="MSC2020">34D30</a> </td> <td class="space"> Structural stability and analogous concepts of solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37-XX" title="MSC2020">37-XX</a> </td> <td class="space"> Dynamical systems and ergodic theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C37" title="MSC2020">34C37</a> </td> <td class="space"> Homoclinic and heteroclinic solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D10" title="MSC2020">34D10</a> </td> <td class="space"> Perturbations of ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astability+of+travelling+waves">stability of travelling waves</a>; <a href="/?q=ut%3Alattice+ordinary+differential+equations">lattice ordinary differential equations</a>; <a href="/?q=ut%3Atime-discretizations+of+lattice+ODEs">time-discretizations of lattice ODEs</a>; <a href="/?q=ut%3ANagumo+equation">Nagumo equation</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 0911.34050" data-ciurl="/ci/01216512" data-biburl="/bibtex/01216512.bib" data-amsurl="/amsrefs/01216512.bib" data-xmlurl="/xml/01216512.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01216512.pdf" title="Zbl 0911.34050 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/10.1006/jdeq.1998.3478" aria-label="DOI for “Traveling waves in lattice dynamical systems”" title="10.1006/jdeq.1998.3478">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">Afraimovich, V. 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