Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions

Details Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions

1998-11-11

arxiv.org/abs/math-ph/9811008v3

Physics

Mathematical Physics

To appear in "Contemporary Mathematics". (Modified as per requests of editor and referees. No serious changes.)

Scientific paper

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.

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