# Compatible Lie brackets and integrable $\sigma$-models

Presented by:
V Sokolov [LITP]
Date:
Wednesday 7th November 2001 - 11:00 to 12:00
Venue:
INI Seminar Room 1
Abstract:
Two classes of integrable nonlinear systems of hyperbolic equations on semi-simple Lie algebras are considered. All these systems are generalizations of the principle chiral model. Each of these systems is related to a pair of compatible Lie brackets. Lax representations for all systems, defined by decompositions of the Lie algebra of Laurant series into a sum of two subalgebras are given. New examples of compatible brackets are presented.