Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry

In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of exponential type is degraded in time, and that the exhibited decay is optimal. I...

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Autores:
León Gil, Carlos Augusto
Tipo de recurso:
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/58837
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/58837
http://bdigital.unal.edu.co/55821/
Palabra clave:
51 Matemáticas / Mathematics
KdV equation
Evolution dispersive equations
Decay properties
Poisson structures
Liouville integrable systems
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_c858e08363889232fb6f67bed92fc127
oai_identifier_str oai:repositorio.unal.edu.co:unal/58837
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network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Isaza Jaramillo, PedroVanhaecke, PolLeón Gil, Carlos Augusto76fc06ad-50cc-4a96-b62f-735befe6007f3002019-07-02T14:53:28Z2019-07-02T14:53:28Z2017-01-27https://repositorio.unal.edu.co/handle/unal/58837http://bdigital.unal.edu.co/55821/In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of exponential type is degraded in time, and that the exhibited decay is optimal. In the second part we will make an exposition on Symplectic and Poisson Geometry with connections in Classical Mechanics to motivate a more abstract view of Poisson structures. With these preliminaries we can then give way to a little digression on Integrable Systems, and discuss the notion of complete integratbility in the sense of LiouvilleMaestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de MatemáticasEscuela de MatemáticasLeón Gil, Carlos Augusto (2017) Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.51 Matemáticas / MathematicsKdV equationEvolution dispersive equationsDecay propertiesPoisson structuresLiouville integrable systemsDecay of solutions of dispersive equations and Poisson brackets in algebraic geometryTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1152203716.2016.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf930992https://repositorio.unal.edu.co/bitstream/unal/58837/1/1152203716.2016.pdf854e719457e93698d24ff5f343a6bd96MD51THUMBNAIL1152203716.2016.pdf.jpg1152203716.2016.pdf.jpgGenerated Thumbnailimage/jpeg4169https://repositorio.unal.edu.co/bitstream/unal/58837/2/1152203716.2016.pdf.jpga53b3d7466344f6e0c545bd54b22d90cMD52unal/58837oai:repositorio.unal.edu.co:unal/588372023-04-19 10:28:11.693Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
title Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
spellingShingle Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
51 Matemáticas / Mathematics
KdV equation
Evolution dispersive equations
Decay properties
Poisson structures
Liouville integrable systems
title_short Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
title_full Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
title_fullStr Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
title_full_unstemmed Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
title_sort Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
dc.creator.fl_str_mv León Gil, Carlos Augusto
dc.contributor.author.spa.fl_str_mv León Gil, Carlos Augusto
dc.contributor.spa.fl_str_mv Isaza Jaramillo, Pedro
Vanhaecke, Pol
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
KdV equation
Evolution dispersive equations
Decay properties
Poisson structures
Liouville integrable systems
dc.subject.proposal.spa.fl_str_mv KdV equation
Evolution dispersive equations
Decay properties
Poisson structures
Liouville integrable systems
description In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of exponential type is degraded in time, and that the exhibited decay is optimal. In the second part we will make an exposition on Symplectic and Poisson Geometry with connections in Classical Mechanics to motivate a more abstract view of Poisson structures. With these preliminaries we can then give way to a little digression on Integrable Systems, and discuss the notion of complete integratbility in the sense of Liouville
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-01-27
dc.date.accessioned.spa.fl_str_mv 2019-07-02T14:53:28Z
dc.date.available.spa.fl_str_mv 2019-07-02T14:53:28Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/58837
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/55821/
url https://repositorio.unal.edu.co/handle/unal/58837
http://bdigital.unal.edu.co/55821/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Matemáticas
Escuela de Matemáticas
dc.relation.references.spa.fl_str_mv León Gil, Carlos Augusto (2017) Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/58837/1/1152203716.2016.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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