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26 April 2024

» arxiv » nlin.SI/0107065

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Hierarchy of (2+1)-dimensional nonlinear Schroedinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras
Saburo Kakei ; Takeshi Ikeda ; Kanehisa Takasaki ;
Date:	30 Jul 2001
Journal:	Annales Henri Poincare 3 (2002) 817-845
Subject:	Exactly Solvable and Integrable Systems; Quantum Algebra; Mathematical Physics; Representation Theory; Differential Geometry \| nlin.SI hep-th math-ph math.DG math.MP math.QA math.RT
Abstract:	The hierarchy structure associated with a (2+1)-dimensional Nonlinear Schroedinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using the language of free fermions. A relation to the self-dual Yang-Mills equation is also discussed.
Source:	arXiv, nlin.SI/0107065
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