This article is cited in 2 papers

Involutive distributions, invariant manifolds, and defining equations

O. V. Kaptsov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

Abstract: We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications.

UDC: 517.956

Received: 26.04.2001

 English version: Siberian Mathematical Journal, 2002, 43:3, 428–438

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