Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

Details Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

2008-03-27

arxiv.org/abs/0803.3866v1

SIGMA 4 (2008), 034, 23 pages

Mathematics

Differential Geometry

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.034

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.

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