NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ON HOMOGENEOUS SPACES

Abstract

The work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some of the integrable nonlinear partial differential equations are given explicitly. In particular the coupled NLS equations on various homogeneous spaces and the coupled modified KdV integro-differential equations are obtained on symmetric spaces.