Document Zbl 1080.86502

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R.</a></div> <h2 class="title"> <strong>The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves.</strong> <i>(English)</i> <a class="label nowrap" href="/1080.86502">Zbl 1080.86502</a> </h2> <div class="source"> <a href="/serials/250" title="Journal Profile">Chaos Solitons Fractals</a> <a href="/?q=in%3A45543" title="Articles in this Issue">5, No. 12, 2623-2637 (1995)</a>. </div> <div class="abstract">Summary: Surface wave data from the Adriatic Sea are analysed in the light of new data analysis techniques which may be viewed as a nonlinear generalization of the ordinary Fourier transform. Nonlinear Fourier analysis as applied herein arises from the exact spectral solution to large classes of nonlinear wave equations which are integrable by the inverse scattering transform (IST). Numerical methods are discussed which allow for implementation of the approach as a tool for the time series analysis of oceanic wave data. The case for unidirectional propagation in shallow water, where integrable nonlinear wave motion is governed by the Korteweg-deVries (KdV) equation with periodic/quasi-periodic boundary conditions, is considered. Numerical procedures given herein can be used to compute a nonlinear Fourier representation for a given measured time series. The nonlinear oscillation modes (the IST ’basis functions’) of KdV obey a linear superposition law, just as do the sine waves of a linear Fourier series. However, the KdV basis functions themselves are highly nonlinear, undergo nonlinear interactions with each other and are distinctly non-sinusoidal. Numerical IST is used to analyse Adriatic Sea data and the concept of nonlinear filtering is applied to improve understanding of the dominant nonlinear interactions in the measured wavetrains.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5006923">Cited in <strong>43</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A86A05" title="MSC2020">86A05</a> </td> <td class="space"> Hydrology, hydrography, oceanography </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A86-08" title="MSC2020">86-08</a> </td> <td class="space"> Computational methods for problems pertaining to geophysics </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><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%3A37M10" title="MSC2020">37M10</a> </td> <td class="space"> Time series analysis of dynamical systems </td> </tr></table> </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 1080.86502" data-ciurl="/ci/05006923" data-biburl="/bibtex/05006923.bib" data-amsurl="/amsrefs/05006923.bib" data-xmlurl="/xml/05006923.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05006923.pdf" title="Zbl 1080.86502 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/10.1016/0960-0779(94)E0118-9" aria-label="DOI for “The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves.”" title="10.1016/0960-0779(94)E0118-9">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">Osborne, A. 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Aha Huliko’a Winter Workshop (1993), University of Hawaii Press) · <a href="/1080.86502" class="nowrap">Zbl 1080.86502</a></td> </tr><tr> <td>[35]</td> <td class="space">Cavaleri, L., Experimental characteristics of wind waves, (Osborne, A. R.; Rizzoli, P. Malanotte, Topics in Ocean Physics (1982), Elsevier: Elsevier Amsterdam) · <a href="/1160.93388" class="nowrap">Zbl 1160.93388</a></td> </tr><tr> <td>[36]</td> <td class="space">Osborne, A. R.; Petti, M., Laboratory-generated, shallow water surface waves: Analysis using the periodic, inverse scattering transform (1993), Submitted for publication</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. 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