Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

Gloria Marí Beffa

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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.

Détail

Keywords: 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.

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