Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
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格拉斯曼函数、非线性波动方程和广义 Schur 函数
DOI：
10.1090/conm/246/03782
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Alex M Kasman
中科院分区：
文献类型：
--
作者：
Alex M Kasman
一组功能的介绍，推广了著名的舒尔多项式和他们的连接到Grasmannian流形。这些功能提供了一种新的方法来构造解决方案的KP系列的非线性偏微分方程。具体地说，正如舒尔多项式被用来扩展tau函数作为一个总和，它表明，这是自然的扩展商的tau函数在这些广义舒尔功能。这种展开式中的系数被发现受到格拉斯曼的Plucker关系的约束。
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.