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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 186–195 (Mi ufa180)  

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

V. A. Dorodnitsyn

Keldysh Institute of Applied Mathematics RAS, Moscow, Russia

Abstract: 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.

Keywords: evolutionary equations, exact solutions, superposition of solutions.

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UDC: 517.9
Received: 27.10.2012
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Citation: V. A. Dorodnitsyn, “The non-autonomous dynamical systems and exact solutions with superposition principle for evolutionary PDEs”, Ufimsk. Mat. Zh., 4:4 (2012), 186–195

Citation in format AMSBIB
\Bibitem{Dor12}
\by V.~A.~Dorodnitsyn
\paper The non-autonomous dynamical systems and exact solutions with superposition principle for evolutionary PDEs
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 4
\pages 186--195
\mathnet{http://mi.mathnet.ru/ufa180}


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