Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

被引：12

作者：

Beffa, Gloria Mari ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53705 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2008年 / 4卷

关键词：

invariant evolutions of curves; Hermitian symmetric spaces; Poisson brackets; differential invariants; projective differential invariants; equations of KdV type; completely integrable PDEs; moving frames; geometric realizations;

D O I：

10.3842/SIGMA.2008.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998), 161-213; 55 (1999), 127-208]. The paper discusses the close connection between different types of geometries and the type of equations they realize. In particular, we describe the direct relation between symmetric spaces and equations of KdV-type, and the possible geometric origins of this connection.

引用

页数：23

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