Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs

Detalhes bibliográficos
Autor(a) principal: Bracciali, Cleonice F. [UNESP]
Data de Publicação: 2017
Outros Autores: Pérez, Teresa E.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.amc.2017.04.005
http://hdl.handle.net/11449/174467
Resumo: We explore the connection between an infinite system of particles in R2 described by a bi-dimensional version of the Toda equations with the theory of orthogonal polynomials in two variables. We define a 2D Toda lattice in the sense that we consider only one time variable and two space variables describing a mesh of interacting particles over the plane. We show that this 2D Toda lattice is related with the matrix coefficients of the three term relations of bivariate orthogonal polynomials associated with an exponential modification of a positive measure. Moreover, block Lax pairs for 2D Toda lattices are deduced.
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spelling Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs2D Toda latticeBlock Lax pairsTwo variable orthogonal polynomialsWe explore the connection between an infinite system of particles in R2 described by a bi-dimensional version of the Toda equations with the theory of orthogonal polynomials in two variables. We define a 2D Toda lattice in the sense that we consider only one time variable and two space variables describing a mesh of interacting particles over the plane. We show that this 2D Toda lattice is related with the matrix coefficients of the three term relations of bivariate orthogonal polynomials associated with an exponential modification of a positive measure. Moreover, block Lax pairs for 2D Toda lattices are deduced.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)European Regional Development FundMinisterio de Economía y CompetitividadDepartamento de Matemática Aplicada IBILCE UNESP – Universidade Estadual PaulistaInstituto de Matemáticas – IEMath-GR & Departamento de Matemática Aplicada Universidad de GranadaDepartamento de Matemática Aplicada IBILCE UNESP – Universidade Estadual PaulistaFAPESP: 2014/22571-2CNPq: 305208/2015-2CNPq: 402939/2016-6European Regional Development Fund: MTM2014-53171-PUniversidade Estadual Paulista (Unesp)Universidad de GranadaBracciali, Cleonice F. [UNESP]Pérez, Teresa E.2018-12-11T17:11:15Z2018-12-11T17:11:15Z2017-09-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article142-155application/pdfhttp://dx.doi.org/10.1016/j.amc.2017.04.005Applied Mathematics and Computation, v. 309, p. 142-155.0096-3003http://hdl.handle.net/11449/17446710.1016/j.amc.2017.04.0052-s2.0-850175122562-s2.0-85017512256.pdf83003224526224670000-0002-6823-4204Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengApplied Mathematics and Computation1,065info:eu-repo/semantics/openAccess2023-12-09T06:19:55Zoai:repositorio.unesp.br:11449/174467Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:50:58.511971Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
title Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
spellingShingle Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
Bracciali, Cleonice F. [UNESP]
2D Toda lattice
Block Lax pairs
Two variable orthogonal polynomials
title_short Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
title_full Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
title_fullStr Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
title_full_unstemmed Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
title_sort Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
author Bracciali, Cleonice F. [UNESP]
author_facet Bracciali, Cleonice F. [UNESP]
Pérez, Teresa E.
author_role author
author2 Pérez, Teresa E.
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidad de Granada
dc.contributor.author.fl_str_mv Bracciali, Cleonice F. [UNESP]
Pérez, Teresa E.
dc.subject.por.fl_str_mv 2D Toda lattice
Block Lax pairs
Two variable orthogonal polynomials
topic 2D Toda lattice
Block Lax pairs
Two variable orthogonal polynomials
description We explore the connection between an infinite system of particles in R2 described by a bi-dimensional version of the Toda equations with the theory of orthogonal polynomials in two variables. We define a 2D Toda lattice in the sense that we consider only one time variable and two space variables describing a mesh of interacting particles over the plane. We show that this 2D Toda lattice is related with the matrix coefficients of the three term relations of bivariate orthogonal polynomials associated with an exponential modification of a positive measure. Moreover, block Lax pairs for 2D Toda lattices are deduced.
publishDate 2017
dc.date.none.fl_str_mv 2017-09-15
2018-12-11T17:11:15Z
2018-12-11T17:11:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.amc.2017.04.005
Applied Mathematics and Computation, v. 309, p. 142-155.
0096-3003
http://hdl.handle.net/11449/174467
10.1016/j.amc.2017.04.005
2-s2.0-85017512256
2-s2.0-85017512256.pdf
8300322452622467
0000-0002-6823-4204
url http://dx.doi.org/10.1016/j.amc.2017.04.005
http://hdl.handle.net/11449/174467
identifier_str_mv Applied Mathematics and Computation, v. 309, p. 142-155.
0096-3003
10.1016/j.amc.2017.04.005
2-s2.0-85017512256
2-s2.0-85017512256.pdf
8300322452622467
0000-0002-6823-4204
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Applied Mathematics and Computation
1,065
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 142-155
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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