Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
Abstract
Description
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear partial differential equations. Specifically, just as the Schur polynomials are used to expand tau-functions as a sum, it is shown that it is natural to expand a quotient of tau-functions in terms of these generalized Schur functions. The coefficients in this expansion are found to be constrained by the Plücker relations of a grassmannian.
To appear in "Contemporary Mathematics". (Modified as per requests of editor and referees. No serious changes.)
To appear in "Contemporary Mathematics". (Modified as per requests of editor and referees. No serious changes.)