Document Zbl 0603.76014

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Fluid Mech.</a> <a href="/?q=in%3A150075" title="Articles in this Issue">150, 395-416 (1985)</a>. </div> <div class="abstract">In existing experiments it is known that the slow evolution of nonlinear deep-water waves exhibits certain asymmetric features. These features lie beyond the realm of applicability of the celebrated cubic Schrödinger equation (CSE), but can be, predicted by weakly nonlinear theories that are not limited to slowly modulated waves (i.e. waves with a narrow spectral band). Alternativly, one may employ the fourth-order equations of <span class="zbmathjax-textit">K. B. Dysthe</span> [Proc. R. Soc. Lond., Ser. A 369, 105-114 (1979; <a href="/0429.76014">Zbl 0429.76014</a>)], which are limited to narrow-banded waves but can nevertheless be solved more easily by a pseudospectral numerical method. Here we report the numerical simulation of three cases with a view to comparing with certain recent experiments and to complement the numerical results obtained by others from the more general equations.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A3974519">Cited in <strong>75</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76B15" title="MSC2020">76B15</a> </td> <td class="space"> Water waves, gravity waves; dispersion and scattering, nonlinear interaction </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q99" title="MSC2020">35Q99</a> </td> <td class="space"> Partial differential equations of mathematical physics and other areas of application </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M99" title="MSC2020">76M99</a> </td> <td class="space"> Basic methods in fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aslow+evolution+of+nonlinear+deep-water+waves">slow evolution of nonlinear deep-water waves</a>; <a href="/?q=ut%3Aweakly+nonlinear+theories">weakly nonlinear theories</a>; <a href="/?q=ut%3Aslowly+modulated+waves">slowly modulated waves</a>; <a href="/?q=ut%3Awaves+with+a+narrow+spectral+band">waves with a narrow spectral band</a>; <a href="/?q=ut%3Afourth-order+equations">fourth-order equations</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0429.76014">Zbl 0429.76014</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 0603.76014" data-ciurl="/ci/03974519" data-biburl="/bibtex/03974519.bib" data-amsurl="/amsrefs/03974519.bib" data-xmlurl="/xml/03974519.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03974519.pdf" title="Zbl 0603.76014 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/10.1017/S0022112085000180" aria-label="DOI for “A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation”" title="10.1017/S0022112085000180">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">Tappert, Lectures Appl. Maths 15 pp 215– (1974)</td> </tr><tr> <td>[2]</td> <td class="space">DOI: 10.1063/1.863708 · <a href="https://doi.org/10.1063/1.863708" class="nowrap">doi:10.1063/1.863708</a></td> </tr><tr> <td>[3]</td> <td class="space">Stiassnie, J. Fluid Mech. 116 pp 207– (1982)</td> </tr><tr> <td>[4]</td> <td class="space">Feir, Proc. R. Soc. Lond. 299 pp 54– (1967)</td> </tr><tr> <td>[5]</td> <td class="space">Dysthe, Proc. R. Soc. Lond. 369 pp 105– (1979)</td> </tr><tr> <td>[6]</td> <td class="space">Crawford, J. Fluid Mech. 105 pp 177– (1981)</td> </tr><tr> <td>[7]</td> <td class="space">DOI: 10.1063/1.861481 · <a href="/0341.76005" class="nowrap">Zbl 0341.76005</a> · <a href="https://doi.org/10.1063/1.861481" class="nowrap">doi:10.1063/1.861481</a></td> </tr><tr> <td>[8]</td> <td class="space">DOI: 10.1017/S0022112071001095 · <a href="/0255.76017" class="nowrap">Zbl 0255.76017</a> · <a href="https://doi.org/10.1017/S0022112071001095" class="nowrap">doi:10.1017/S0022112071001095</a></td> </tr><tr> <td>[9]</td> <td class="space">DOI: 10.1017/S0022112070000988 · <a href="/0221.76005" class="nowrap">Zbl 0221.76005</a> · <a href="https://doi.org/10.1017/S0022112070000988" class="nowrap">doi:10.1017/S0022112070000988</a></td> </tr><tr> <td>[10]</td> <td class="space">Bryant, J. Fluid Mech. 114 pp 443– (1982)</td> </tr><tr> <td>[11]</td> <td class="space">DOI: 10.1017/S002211206700045X · <a href="/0144.47101" class="nowrap">Zbl 0144.47101</a> · <a href="https://doi.org/10.1017/S002211206700045X" class="nowrap">doi:10.1017/S002211206700045X</a></td> </tr><tr> <td>[12]</td> <td class="space">DOI: 10.1016/0165-2125(84)90043-X · <a href="/0565.76020" class="nowrap">Zbl 0565.76020</a> · <a href="https://doi.org/10.1016/0165-2125(84)90043-X" class="nowrap">doi:10.1016/0165-2125(84)90043-X</a></td> </tr><tr> <td>[13]</td> <td class="space">DOI: 10.1063/1.863319 · <a href="/0477.76024" class="nowrap">Zbl 0477.76024</a> · <a href="https://doi.org/10.1063/1.863319" class="nowrap">doi:10.1063/1.863319</a></td> </tr><tr> <td>[14]</td> <td class="space">DOI: 10.1063/1.862025 · <a href="https://doi.org/10.1063/1.862025" class="nowrap">doi:10.1063/1.862025</a></td> </tr><tr> <td>[15]</td> <td class="space">Melville, J. 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Mech. 22 pp 67– (1982)</td> </tr><tr> <td>[23]</td> <td class="space">DOI: 10.1063/1.862394 · <a href="https://doi.org/10.1063/1.862394" class="nowrap">doi:10.1063/1.862394</a></td> </tr><tr> <td>[24]</td> <td class="space">DOI: 10.1063/1.1694844 · <a href="/0294.76011" class="nowrap">Zbl 0294.76011</a> · <a href="https://doi.org/10.1063/1.1694844" class="nowrap">doi:10.1063/1.1694844</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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