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The reducibility of partially invariant solutions of systems of partial differential equations

Published online by Cambridge University Press:  26 September 2008

Jeffrey Ondich
Jeffrey Ondich
Affiliation:
Department of Mathematics and Computer Science, Carleton College, Northfield, MN 55057-40254, USA
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Abstract

Ovsiannikov's partially invariant solutions of differential equations generalize Lie's group invariant solutions. A partially invariant solution is only interesting if it cannot be discovered more readily as an invariant solution. Roughly, a partially invariant solution that can be discovered more directly by Lie's method is said to be reducible. In this paper, I develop conditions under which a partially invariant solution or a class of such solutions must be reducible, and use these conditions both to obtain non-reducible solutions to a system of hyperbolic conservation laws, and to demonstrate that some systems have no non-reducible solutions. I also demonstrate that certain elliptic systems have no non-reducible solutions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 4 , August 1995 , pp. 329 - 354
Copyright
Copyright © Cambridge University Press 1995

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