Characteristic Lie rings of differential equations

The characteristic Lie rings corresponding to hyperbolic type equations are considered. Possible applications of this concept to the problem of integrable classification of systems of the hyperbolic type partial differential equations with more than two characteristic destinations, evolutionary type equations and ordinary differential equations are briefly discussed. The widely known models of mathematical physics as well as the system of “n”-wave equations, the Korteweg-de Vries equation, the Burgers equation and the first Painlevé equation are considered as illustrative examples.