Extended Relativistic Toda Lattice, L-Orthogonal Polynomials and Associated Lax Pair

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dc.contributor.authorBracciali, Cleonice F. [UNESP]
dc.contributor.authorSilva, Jairo S.
dc.contributor.authorSri Ranga, A. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Federal do Maranhão
dc.date.accessioned2019-10-06T15:27:05Z
dc.date.available2019-10-06T15:27:05Z
dc.date.issued2018-01-01
dc.description.abstractWhen a measure Ψ(x) on the real line is subjected to the modification dΨ( t )(x) = e− t xdΨ(x) , then the coefficients of the recurrence relation of the orthogonal polynomials in x with respect to the measure Ψ( t )(x) are known to satisfy the so-called Toda lattice formulas as functions of t. In this paper we consider a modification of the form e− t ( p x + q / x ) of measures or, more generally, of moment functionals, associated with orthogonal L-polynomials and show that the coefficients of the recurrence relation of these L-orthogonal polynomials satisfy what we call an extended relativistic Toda lattice. Most importantly, we also establish the so called Lax pair representation associated with this extended relativistic Toda lattice. These results also cover the (ordinary) relativistic Toda lattice formulations considered in the literature by assuming either p= 0 or q= 0. However, as far as Lax pair representation is concern, no complete Lax pair representations were established before for the respective relativistic Toda lattice formulations. Some explicit examples of extended relativistic Toda lattice and Langmuir lattice are also presented. As further results, the lattice formulas that follow from the three term recurrence relations associated with kernel polynomials on the unit circle are also established.en
dc.description.affiliationDepartamento de Matemática Aplicada UNESP–Univ Estadual Paulista
dc.description.affiliationDepartamento de Matemática Universidade Federal do Maranhão
dc.description.affiliationUnespDepartamento de Matemática Aplicada UNESP–Univ Estadual Paulista
dc.identifierhttp://dx.doi.org/10.1007/s10440-018-00229-x
dc.identifier.citationActa Applicandae Mathematicae.
dc.identifier.doi10.1007/s10440-018-00229-x
dc.identifier.issn1572-9036
dc.identifier.issn0167-8019
dc.identifier.lattes8300322452622467
dc.identifier.orcid0000-0002-6823-4204
dc.identifier.scopus2-s2.0-85058120871
dc.identifier.urihttp://hdl.handle.net/11449/187153
dc.language.isoeng
dc.relation.ispartofActa Applicandae Mathematicae
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectKernel polynomials on the unit circle
dc.subjectL-orthogonal polynomials
dc.subjectLax pairs
dc.subjectRelativistic Toda lattice
dc.titleExtended Relativistic Toda Lattice, L-Orthogonal Polynomials and Associated Lax Pairen
dc.typeArtigo
unesp.author.lattes8300322452622467[1]
unesp.author.orcid0000-0002-6823-4204[1]

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