Persistence of periodic traveling waves and Abelian integrals

Preprint

Detalles Bibliográficos
Autores: Gasull Embid, Armengol, Geyer, Anna, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: informe técnico
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/341932
Acceso en línea:https://hdl.handle.net/2117/341932
Access Level:acceso abierto
Palabra clave:Differential equations, Partial
Traveling wave
Abelian integral
Melnikov-Poincaré-Pontryagin function
Periodic orbit
Limit cycle
Bifurcation
Equacions diferencials parcials
Classificació AMS::35 Partial differential equations::35C Representations of solutions
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
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oai_identifier_str oai:upcommons.upc.edu:2117/341932
network_acronym_str ES
network_name_str España
repository_id_str
spelling Persistence of periodic traveling waves and Abelian integralsGasull Embid, ArmengolGeyer, AnnaMañosa Fernández, Víctor|||0000-0002-5082-3334Differential equations, PartialTraveling waveAbelian integralMelnikov-Poincaré-Pontryagin functionPeriodic orbitLimit cycleBifurcationEquacions diferencials parcialsClassificació AMS::35 Partial differential equations::35C Representations of solutionsClassificació AMS::34 Ordinary differential equations::34C Qualitative theoryClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integralsPreprintIt is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. In this paper we address the problem of persistence of TWS of a given PDE under small perturbations. Our main results deal with the situation where the associated ODE has a center and, as a consequence, the original PDE has a continuum of periodic traveling wave solutions. We prove that the TWS that persist are controlled by the zeroes of some Abelian integrals. We apply our results to several famous PDE, like the Ostrovsky, Klein-Gordon, sine-Gordon, Korteweg-de Vries, Rosenau-Hyman, Camassa-Holm, and Boussinesq equations20212021-03-1020212021-03-18reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/341932reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3419322026-05-27T15:37:01Z
dc.title.none.fl_str_mv Persistence of periodic traveling waves and Abelian integrals
title Persistence of periodic traveling waves and Abelian integrals
spellingShingle Persistence of periodic traveling waves and Abelian integrals
Gasull Embid, Armengol
Differential equations, Partial
Traveling wave
Abelian integral
Melnikov-Poincaré-Pontryagin function
Periodic orbit
Limit cycle
Bifurcation
Equacions diferencials parcials
Classificació AMS::35 Partial differential equations::35C Representations of solutions
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
title_short Persistence of periodic traveling waves and Abelian integrals
title_full Persistence of periodic traveling waves and Abelian integrals
title_fullStr Persistence of periodic traveling waves and Abelian integrals
title_full_unstemmed Persistence of periodic traveling waves and Abelian integrals
title_sort Persistence of periodic traveling waves and Abelian integrals
dc.creator.none.fl_str_mv Gasull Embid, Armengol
Geyer, Anna
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author Gasull Embid, Armengol
author_facet Gasull Embid, Armengol
Geyer, Anna
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author_role author
author2 Geyer, Anna
Mañosa Fernández, Víctor|||0000-0002-5082-3334
author2_role author
author
dc.subject.none.fl_str_mv Differential equations, Partial
Traveling wave
Abelian integral
Melnikov-Poincaré-Pontryagin function
Periodic orbit
Limit cycle
Bifurcation
Equacions diferencials parcials
Classificació AMS::35 Partial differential equations::35C Representations of solutions
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
topic Differential equations, Partial
Traveling wave
Abelian integral
Melnikov-Poincaré-Pontryagin function
Periodic orbit
Limit cycle
Bifurcation
Equacions diferencials parcials
Classificació AMS::35 Partial differential equations::35C Representations of solutions
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
description Preprint
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-03-10
2021
2021-03-18
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/341932
url https://hdl.handle.net/2117/341932
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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