Author: Arthemy V. Kiselev

In this paper, we investigate the algebraic and geometric properties of the hyperbolic Toda equations associated with nondegenerate symmetrizable matrices K. A hierarchy of analogs to the potential modified Korteweg-de Vries equation is constructed, and its relation with the hierarchy for the Korteweg-de Vries equation is established. Group-theoretic structures for the dispersionless (2+1)-dimensional Toda equation are obtained. Geometric properties of the multi-component nonlinear Schrödinger equation type systems are described.

134 pages, AmS-LaTeX (LaTeX-2e).

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