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Уфимский математический журнал, 2012, том 4, выпуск 4, страницы 186–195
(Mi ufa180)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
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
Аннотация:
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.
Ключевые слова:
evolutionary equations, exact solutions, superposition of solutions.
Поступила в редакцию: 27.10.2012
Образец цитирования:
V. A. Dorodnitsyn, “The non-autonomous dynamical systems and exact solutions with superposition principle for evolutionary PDEs”, Уфимск. матем. журн., 4:4 (2012), 186–195
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ufa180 https://www.mathnet.ru/rus/ufa/v4/i4/p186
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Страница аннотации: | 261 | PDF полного текста: | 103 | Список литературы: | 41 | Первая страница: | 1 |
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