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On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients

In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first cas...

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Detalles Bibliográficos
Autores principales: Abdel-Gawad, Hamdy I., Osman, Mohamed
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4506973/
https://www.ncbi.nlm.nih.gov/pubmed/26199750
http://dx.doi.org/10.1016/j.jare.2014.02.004
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author Abdel-Gawad, Hamdy I.
Osman, Mohamed
author_facet Abdel-Gawad, Hamdy I.
Osman, Mohamed
author_sort Abdel-Gawad, Hamdy I.
collection PubMed
description In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s.
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spelling pubmed-45069732015-07-21 On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients Abdel-Gawad, Hamdy I. Osman, Mohamed J Adv Res Original Article In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s. Elsevier 2015-07 2014-02-25 /pmc/articles/PMC4506973/ /pubmed/26199750 http://dx.doi.org/10.1016/j.jare.2014.02.004 Text en © 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University. http://creativecommons.org/licenses/by-nc-nd/3.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
spellingShingle Original Article
Abdel-Gawad, Hamdy I.
Osman, Mohamed
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title_full On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title_fullStr On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title_full_unstemmed On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title_short On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
title_sort on shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4506973/
https://www.ncbi.nlm.nih.gov/pubmed/26199750
http://dx.doi.org/10.1016/j.jare.2014.02.004
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