{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T08:07:02Z","timestamp":1771920422857,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T00:00:00Z","timestamp":1698278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau\u2013Kawahara\u2013RLW model established by coupling the generalized Rosenau\u2013Kawahara and Rosenau\u2013RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.<\/jats:p>","DOI":"10.3390\/sym15111980","type":"journal-article","created":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T03:33:51Z","timestamp":1698377631000},"page":"1980","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Solitary Wave Propagation of the Generalized Rosenau\u2013Kawahara\u2013RLW Equation in Shallow Water Theory with Surface Tension"],"prefix":"10.3390","volume":"15","author":[{"given":"Akeel","family":"AL-saedi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education, Misan University, Misan 62001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"Omid","family":"Nikan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran 16846-13114, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2257-1798","authenticated-orcid":false,"given":"Zakieh","family":"Avazzadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEG, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,26]]},"reference":[{"key":"ref_1","first-page":"69","article-title":"First evidence of paleo-tsunami deposits of a major historic event in Ecuador","volume":"33","author":"Chunga","year":"2014","journal-title":"J. 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