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

Saburo Kakei; Takeshi Ikeda; Kanehisa Takasaki

doi:10.1007/s00023-002-8638-1

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arXiv · nlin/0107065

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

Saburo Kakei·Takeshi Ikeda·Kanehisa Takasaki

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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.

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Saburo Kakei, Takeshi Ikeda, Kanehisa Takasaki. 2001-07-30. Hierarchy of (2+1)-dimensional nonlinear Schroedinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras. https://doi.org/10.1007/s00023-002-8638-1

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