Reducible KAM Tori for the Degasperis-Procesi equation

We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash–Moser nonlinear iteration, pseudo differential calculus and normal...

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Detalles Bibliográficos
Autores: Feola, Roberto, Giuliani, Filippo, Procesi, Michela
Tipo de recurso: artículo
Fecha de publicación:2020
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:2117/332387
Acceso en línea:https://hdl.handle.net/2117/332387
https://dx.doi.org/10.1007/s00220-020-03788-z
Access Level:acceso abierto
Palabra clave:Hamiltonian systems
Sistemes hamiltonians
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Reducible KAM Tori for the Degasperis-Procesi equationFeola, RobertoGiuliani, FilippoProcesi, MichelaHamiltonian systemsSistemes hamiltoniansÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash–Moser nonlinear iteration, pseudo differential calculus and normal form techniques. In the present case the complicated symplectic structure, the weak dispersive effects of the linear flow and the presence of strong resonant interactions require a novel set of ideas. The main points are to exploit the integrability of the unperturbed equation, to look for special wave packet solutions and to perform a very careful algebraic analysis of the resonances. Our approach is quite general and can be applied also to other 1d integrable PDEs. We are confident for instance that the same strategy should work for the Camassa–Holm equation.Peer Reviewed20202020-06-1920202020-11-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/332387https://dx.doi.org/10.1007/s00220-020-03788-zreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3323872026-05-27T15:37:01Z
dc.title.none.fl_str_mv Reducible KAM Tori for the Degasperis-Procesi equation
title Reducible KAM Tori for the Degasperis-Procesi equation
spellingShingle Reducible KAM Tori for the Degasperis-Procesi equation
Feola, Roberto
Hamiltonian systems
Sistemes hamiltonians
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Reducible KAM Tori for the Degasperis-Procesi equation
title_full Reducible KAM Tori for the Degasperis-Procesi equation
title_fullStr Reducible KAM Tori for the Degasperis-Procesi equation
title_full_unstemmed Reducible KAM Tori for the Degasperis-Procesi equation
title_sort Reducible KAM Tori for the Degasperis-Procesi equation
dc.creator.none.fl_str_mv Feola, Roberto
Giuliani, Filippo
Procesi, Michela
author Feola, Roberto
author_facet Feola, Roberto
Giuliani, Filippo
Procesi, Michela
author_role author
author2 Giuliani, Filippo
Procesi, Michela
author2_role author
author
dc.subject.none.fl_str_mv Hamiltonian systems
Sistemes hamiltonians
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Hamiltonian systems
Sistemes hamiltonians
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash–Moser nonlinear iteration, pseudo differential calculus and normal form techniques. In the present case the complicated symplectic structure, the weak dispersive effects of the linear flow and the presence of strong resonant interactions require a novel set of ideas. The main points are to exploit the integrability of the unperturbed equation, to look for special wave packet solutions and to perform a very careful algebraic analysis of the resonances. Our approach is quite general and can be applied also to other 1d integrable PDEs. We are confident for instance that the same strategy should work for the Camassa–Holm equation.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-06-19
2020
2020-11-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/332387
https://dx.doi.org/10.1007/s00220-020-03788-z
url https://hdl.handle.net/2117/332387
https://dx.doi.org/10.1007/s00220-020-03788-z
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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 15,301629

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