Multivariate Toda hierarchies and biorthogonal polynomials

A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to multivariate biorthogonal polynomials is discussed. This integrable hierarchy is associated with non-standard multivariate biorthogonality. Wave and Baker functions, linear equations, Lax and Zakharov–Shabat equ...

Descripción completa

Detalles Bibliográficos
Autores: Ariznabarreta García de Cortázar, Gerardo, Mañas Baena, Manuel Enrique
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71532
Acceso en línea:https://hdl.handle.net/20.500.14352/71532
Access Level:acceso abierto
Palabra clave:51-73
Multivariate orthogonal polynomials
Multivariate Toda hierarchy
Generalized KP equations
Bilinear equations
Borel–Gauss factorization
Quasi-determinants
Física-Modelos matemáticos
Física matemática
Descripción
Sumario:A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to multivariate biorthogonal polynomials is discussed. This integrable hierarchy is associated with non-standard multivariate biorthogonality. Wave and Baker functions, linear equations, Lax and Zakharov–Shabat equations, KP type equations, appropriate reductions, Darboux or linear spectral transformations, and bilinear equations involving linear spectral transformations are presented.