Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 48-57
Characteristic Lie rings of differential equations.
G\"urses M., Habibullin I.T., Zhiber A.V.
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In the work the characteristic Lie rings are considered corresponding to the hyperbolic type equations. 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, Korteweg-de Vries equation, Burgers equation and the first Painlevé equation are cosidered as illustrative examples .