This article is cited 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.

UDC: 517.9

Received: 27.10.2012

Language: English