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Ufimskii Matematicheskii Zhurnal, 2012, Volume 4, Issue 4, Pages 186–195
(Mi ufa180)
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This article is cited in 3 scientific papers (total in 3 papers)
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.
Received: 27.10.2012
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
Linking options:
https://www.mathnet.ru/eng/ufa180 https://www.mathnet.ru/eng/ufa/v4/i4/p186
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Abstract page: | 245 | Full-text PDF : | 90 | References: | 35 | First page: | 1 |
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