Article

    Ufa Mathematical Journal
    Volume 4, Number 4, pp. 181-190

    The non-autonomous dynamical systems and exact solutions with superposition principle for evolutionary PDEs


    Dorodnitsyn V.A.

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    In the present article we introduce a new application of S.Lie's non-autonomous dynamical systems with the generalized separation of variables in right hand-sides. We consider non-autonomous dynamical equations as some sort of external action on a given evolution equation, which transforms a subset of solutions into itself. The goal of our approach is to find a subset of solutions of an evolution equation with a superposition principle. This leads to an integration of ordinary differential equations in a process of constructing exact solutions of PDEs. In this paper we consider the application of the most simple one-dimensional case of the Lie theorem.