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...
| Autores: | , , , |
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| 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 |
| 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. |
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