Loop algebra and visaoro symmetries of integrable hierarchies of KP type

We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models cKP R, M (generalized AKNS hierarchies), and their multi component (matrix) generalizations. Any cKP R, M integrable hierarchy is shown to possess (Formula presented.) loop algebra (ad...

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Detalles Bibliográficos
Autores: Aratyn, H., Gomes, J. F. [UNESP], Nissimov, E., Pacheva, S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2001
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/223897
Acceso en línea:http://dx.doi.org/10.1080/00036810108840937
http://hdl.handle.net/11449/223897
Access Level:acceso abierto
Palabra clave:35Q55
58F07
KP hierarchy
Loop algebra
Symmetry flows
Virasoro algebra
Descripción
Sumario:We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models cKP R, M (generalized AKNS hierarchies), and their multi component (matrix) generalizations. Any cKP R, M integrable hierarchy is shown to possess (Formula presented.) loop algebra (additional) symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a non trivial modification of the known Orlov Schulman construction for the general unconstrained KP hierarchy. Multi component KP hierarchies are identified as ordinary (scalar) one component KP hierarchies supplemented with the Cartan subalgebra of the additional symmetry algebra, which provides the basis of a new method for construction of soliton like solutions. Davey Stewartson and N wave resonant systems arise as symmetry flows of ordinary CKPR, M hierarchies. © 2001, Taylor & Francis Group, LLC.