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Hierarchy of (2+1)-dimensional nonlinear Schroedinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras

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arxiv nlin/0107065 v1 pith:55KY6RMD submitted 2001-07-30 nlin.SI hep-thmath-phmath.DGmath.MPmath.QAmath.RT

Saburo Kakei , Takeshi Ikeda , Kanehisa Takasaki This is my paper · ORCID
classification nlin.SIhep-thmath-phmath.DGmath.MPmath.QAmath.RT
keywords equationhierarchyalgebrasdimensionaldiscussednonlinearrelationschroedinger
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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.

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