**DIPS 6/2004**[tex source, PostScript, PDF file, dvi]-
**Title:**Methods of geometry of differential equations in analysis of the integrable field theory models.**Author:**Arthemy V. KiselevIn 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.

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