Geodesic
Two-dimensional nonlinear equations of the string type and their complete integration
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 323-337 
A. N. Leznov; M. V. Saveliev. Two-dimensional nonlinear equations of the string type and their complete integration. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 323-337. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a0/
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     title = {Two-dimensional nonlinear equations of the string type and their complete integration},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The general algebraic construction of the authors [1] is used in an investigation of two-dimensional nonlinear dynamical systems associated by a Lax type representation with the local part of an arbitrary graded Lie algebra. These systems contain as simplest case [for simple finite- and infinite-dimensional (of finite growth) Lie algebras] the generalized two-dimensionalized Toda chain. General (in the sense of the Goursat problem) solutions of the equations characterized by the necessary number of arbitrary functions are constructed. Their structure is illustrated by a detailed consideration of “string” type systems associated with a definite embedding of a three-dimensional subalgebra in the algebra $B_n$. The geometrical interpretation of the corresponding equations is discussed.

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