Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
Mathematical Physics
2007-05-23 v3 Algebraic Geometry
Analysis of PDEs
Functional Analysis
math.MP
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 Pl\"ucker relations of a grassmannian.
Cite
@article{arxiv.math-ph/9811008,
title = {Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions},
author = {Alex Kasman},
journal= {arXiv preprint arXiv:math-ph/9811008},
year = {2007}
}
Comments
To appear in "Contemporary Mathematics". (Modified as per requests of editor and referees. No serious changes.)