On Some Integrable Generalisations of the Continuous Toda System

Abstract

In the present paper we obtain some integrable generalisations of the continuous Toda system generated by a flat connection form taking values in higher grading subspaces of the algebra of the area--preserving diffeomorphism of the torus $T^2$, and construct their general solutions. The grading condition which we use here, imposed on the connection, can be realised in terms of some holomorphic distributions on the corresponding homogeneous spaces.

12 pages, no figures, LaTeX file