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Theory Dyn. Syst.</a> <a href="/?q=in%3A511305" title="Articles in this Issue">23, No. 4, Paper No. 184, 11 p. (2024)</a>; correction ibid. 23, Suppl. 1, Paper No. 300, 2 p. (2024). </div> <div class="abstract">Summary: These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7851492">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7851492">Cited in <strong>15</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35C08" title="MSC2020">35C08</a> </td> <td class="space"> Soliton solutions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A22" title="MSC2020">35A22</a> </td> <td class="space"> Transform methods (e.g., integral transforms) applied to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Along+waves+in+shallow+water">long waves in shallow water</a>; <a href="/?q=ut%3A%282%2B1%29-dimensional+generalized+Broer-Kaup+system">(2+1)-dimensional generalized Broer-Kaup system</a>; <a href="/?q=ut%3Aauto-B%C3%A4cklund+transformation">auto-Bäcklund transformation</a>; <a href="/?q=ut%3Asoliton">soliton</a>; <a href="/?q=ut%3Ascaling+transformation">scaling transformation</a>; <a href="/?q=ut%3Ahetero-B%C3%A4cklund+transformation">hetero-Bäcklund transformation</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 1543.35067" data-ciurl="/ci/07851492" data-biburl="/bibtex/07851492.bib" data-amsurl="/amsrefs/07851492.bib" data-xmlurl="/xml/07851492.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07851492.pdf" title="Zbl 1543.35067 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/s12346-024-01025-9" aria-label="DOI for “In the shallow water: auto-Bäcklund, hetero-Bäcklund and scaling transformations via a (2+1)-dimensional generalized Broer-Kaup system”" title="10.1007/s12346-024-01025-9">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">Rabie, WB; Khalil, TA; Badra, N.; Ahmed, HM; Mirzazadeh, M.; Hashemi, MS, Soliton solutions and other solutions to the (4+1)-dimensional Davey-Stewartson-Kadomtsev-Petviashvili equation using modified extended mapping method, Qual. 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