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Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions

Alex Kasman
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Abstract

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.

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Alex Kasman. 1999-02-26. Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions. https://arxiv.org/abs/math-ph/9811008

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