RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Ufimsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (413 kB)
References: PDF file   HTML file
UDC: 517.9
Language:

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}