%0 Journal Article
%T Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
%A Alex Kasman
%J Physics
%D 1998
%I arXiv
%X 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 Pl\"ucker relations of a grassmannian.
%U http://arxiv.org/abs/math-ph/9811008v3