Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/6002 |
Resumo: | An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equationsBoussinesq differential equationsAsymptotic methodsTravelling wave solutionsSolitonsAn improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.SPRINGERRCIPLPereira, P. J. S.Lopes, Nuno DavidTrabucho, L.2016-04-15T15:57:33Z2015-102015-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6002engPEREIRA, P. J. S.; LOPES, N. D.; TRABUCHO, L. - Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations. Nonlinear Dynamics. ISSN. 0924-090X. Vol. 82, N.º 1-2 (2015), pp. 783-8180924-090X10.1007/s11071-015-2196-9metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:14Zoai:repositorio.ipl.pt:10400.21/6002Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:13.026068Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
title |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
spellingShingle |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations Pereira, P. J. S. Boussinesq differential equations Asymptotic methods Travelling wave solutions Solitons |
title_short |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
title_full |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
title_fullStr |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
title_full_unstemmed |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
title_sort |
Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations |
author |
Pereira, P. J. S. |
author_facet |
Pereira, P. J. S. Lopes, Nuno David Trabucho, L. |
author_role |
author |
author2 |
Lopes, Nuno David Trabucho, L. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Pereira, P. J. S. Lopes, Nuno David Trabucho, L. |
dc.subject.por.fl_str_mv |
Boussinesq differential equations Asymptotic methods Travelling wave solutions Solitons |
topic |
Boussinesq differential equations Asymptotic methods Travelling wave solutions Solitons |
description |
An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-10 2015-10-01T00:00:00Z 2016-04-15T15:57:33Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.21/6002 |
url |
http://hdl.handle.net/10400.21/6002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
PEREIRA, P. J. S.; LOPES, N. D.; TRABUCHO, L. - Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations. Nonlinear Dynamics. ISSN. 0924-090X. Vol. 82, N.º 1-2 (2015), pp. 783-818 0924-090X 10.1007/s11071-015-2196-9 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
SPRINGER |
publisher.none.fl_str_mv |
SPRINGER |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133409825521664 |