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Existence, Stability and Computation of Periodic Waves for a Generalized Benney-Luke Equation.

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dc.contributor.authorMuñoz Grajales, Juan Carlos
dc.contributor.corporatenameUniversidad del Valle (Cali, Colombia)spa
dc.contributor.researchgroupEDPG-Univalle-Erm
dc.coverage.projectdates2004-2006spa
dc.date.accessioned2020-10-13T18:40:53Z
dc.date.accessioned2020-12-17T23:25:34Z
dc.date.available2020-10-13T18:40:53Z
dc.date.available2020-12-17T23:25:34Z
dc.date.issued2006-12
dc.description.abstractIn this work we consider a model which describes the propagation of surface long waves with small amplitude on a fluid of constant depth and including the effect of surface tension. We also analyze the interaction of a travelling wave with a forcing submersed topography. In this case, the model adopted is a generalization of the Benney-Luke model (gBL) which includes a forcing term coming from the topography named (fBL). The gBL model has been considered by J. Quintero in the paper ¨Existence and Analyticity of Lumps Solutions for Generalized Benney - Luke Equations¨(Rev. Col. Mat.. 36, 2002) . Quintero proved the existence and analyticity of lump solutions for the gBL equation. The fBL model including the forcing topography was derived by Mileswki and Keller in the papers ¨ Three dimensional surface waves¨( Stud. Appl. Math., 37, pp. 149-166, 1996) and ¨the generation and evolution of lump solitary waves in surface-tension-dominated flows¨(SIAM J. Appl. Math., Vol. 61, No. 3, pp. 731-750, 2000). Berger and Milewski studied the propagation of a two-dimensional lump solitary wave over a localized topographical feature (a bump), when the surface tension is significant and near the critical shallow water speed. However there is a lack of mathematical theory for existence and orbital stability of Cnoidal and Dnoidal wave solutions to equation (gBL) in constant depth. Furthermore to our knowledge, periodic travelling waves propagating over more complicated topographical profiles have not been yet considered. The first specific objective of this project is to prove existence of 1-D T-periodic travelling waves (Cnoidal and Dnoidal solutions) governed by the (gBL) equation. It is also expected to analyze the behavior of these periodic solutions as a function of the period T and to prove its orbital stability. The main theoretical results to be used are the Concentration-Compactness Principle, Grillakis-Shatah-Strauss' theory and the Lyapunov method to prove orbital stability. The second specific objective is the numerical solution to the equation (gBL) in 1D and 2D, including the effect of a submersed rough topography in the wave scattering. To achieve this objective, we will implement an efficient pseudospectral solver to compute with good accuracy solutions of the gBL and fBL equations over a large time interval. In addition to the theoretical results, we expect to generate a mathematical activity in applied analysis area in Colombia and inside of the Mathematics Department at Universidad del Valle by offering novel thesis problems to undergraduate and graduate students in our academic programs.spa
dc.format.extent332 páginas.spa
dc.identifier.instnameColcienciasspa
dc.identifier.reponameRepositorio Colcienciasspa
dc.identifier.repourlhttp://colciencias.metabiblioteca.com.cospa
dc.identifier.urihttps://colciencias.metadirectorio.org/handle/11146/38832
dc.language.isoengspa
dc.relation.ispartofseriesInforme;
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.accessrightshttp://purl.org/coar/access_right/c_abf2spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.accessrightshttp://purl.org/coar/access_right/c_abf2spa
dc.rights.creativecommonshttps://creativecommons.org/licenses/by/4.0/spa
dc.subject.proposalCompactnessspa
dc.subject.proposalIrregular topographyspa
dc.subject.proposalOrbital Stabilityspa
dc.subject.proposalSolitary wavesspa
dc.subject.proposalSpectral methodsspa
dc.subject.proposalStiffnessspa
dc.titleExistence, Stability and Computation of Periodic Waves for a Generalized Benney-Luke Equation.spa
dc.typeInforme de investigaciónspa
dc.type.coarhttp://purl.org/coar/resource_type/c_93fcspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/reportspa
dc.type.redcolhttps://purl.org/redcol/resource_type/PIDspa
dc.type.versioninfo:eu-repo/semantics/submittedVersionspa
dc.type.versionhttp://purl.org/coar/version/c_71e4c1898caa6e32spa
dc.type.versioninfo:eu-repo/semantics/submittedVersionspa
dc.type.versionhttp://purl.org/coar/version/c_71e4c1898caa6e32spa
dcterms.audienceEstudiantes, Profesores, Comunidad científica colombiana, etc.spa
dspace.entity.typePublication
oaire.awardnumber11060516858spa
oaire.funderidentifier.colciencias252-2004
oaire.fundernameDepartamento Administrativo de Ciencia, Tecnología e Innovación [CO] Colcienciasspa
oaire.fundingstreamPrograma Nacional en Ciencias Básicasspa
oaire.objetivesTo prove the existence, uniqueness and orbital stability of 1D periodic travelling wave solutions for the generalized Benney-Luke equation (gBL) and compute numerically the solutions to the forced Benney-Luke equation (fBL).spa

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