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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier
2015
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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. |
format | Online Article Text |
id | pubmed-4506973 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | Elsevier |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT abdelgawadhamdyi onshallowwaterwavesinamediumwithtimedependentdispersionandnonlinearitycoefficients AT osmanmohamed onshallowwaterwavesinamediumwithtimedependentdispersionandnonlinearitycoefficients |