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

摘要

The hierarchy structure associated with a (2+1)-dimensional NonlinearSchroedinger equation is discussed as an extension of the theory of the KPhierarchy. Several methods to construct special solutions are given. Therelation between the hierarchy and a representation of toroidal Lie algebrasare established by using the language of free fermions. A relation to theself-dual Yang-Mills equation is also discussed.