The hierarchy structure associated with a (2 + 1)-dimensional Nonlinear Schrödinger 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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics