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Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

2015-10Journal article Restricted access
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dc.contributor.authorPereira, P. J. S.
dc.contributor.authorLopes, Nuno David
dc.contributor.authorTrabucho, L.
dc.date.accessioned2016-04-15T15:57:33Z
dc.date.available2016-04-15T15:57:33Z
dc.date.issued2015-10
dc.description.abstractAn 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.pt_PT
dc.identifier.citationPEREIRA, 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. 783-818pt_PT
dc.identifier.doi10.1007/s11071-015-2196-9pt_PT
dc.identifier.issn0924-090X
dc.identifier.issn1573-269X
dc.identifier.urihttp://hdl.handle.net/10400.21/6002
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSPRINGERpt_PT
dc.relationPTDC/MAT109973/2009pt_PT
dc.relationCentre of Physics and Technological Research
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s11071-015-2196-9pt_PT
dc.subjectBoussinesq differential equationspt_PT
dc.subjectAsymptotic methodspt_PT
dc.subjectTravelling wave solutionspt_PT
dc.subjectSolitonspt_PT
dc.titleSoliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equationspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCentre of Physics and Technological Research
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/PEst-OE%2FFIS%2FUI0068%2F2014/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PEst-OE%2FMAT%2FUI0209%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F00297%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FFIS%2F00068%2F2013/PT
oaire.citation.endPage818pt_PT
oaire.citation.issue1-2pt_PT
oaire.citation.startPage783pt_PT
oaire.citation.volume82pt_PT
oaire.fundingStream5876
oaire.fundingStream3599-PPCDT
oaire.fundingStream5876
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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