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New exact solutions of the Boussinesq equation

Published online by Cambridge University Press:  16 July 2009

Peter A. Clarkson
Peter A. Clarkson
Affiliation:
Department of Mathematics, University of Exeter, Exeter, EX4 4QE, England
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Abstract

In this paper new exact solutions are derived for the physically and mathematically significant Boussinesq equation. These are obtained in two different ways: first, by generating exact solutions to the ordinary differential equations which arise from (classical and nonclassical) similarity reductions of the Boussinesq equation (these ordinary differential equations are solvable in terms of the first, second and fourth Painlevé equations); and second, by deriving new space-independent similarity reductions of the Boussinesq equation. Extensive sets of exact solutions for both the second and fourth Painlevé equations are also generated. The symbolic manipulation language MACSYMA is employed to facilitate the calculations involved.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 3 , September 1990 , pp. 279 - 300
Copyright
Copyright © Cambridge University Press 1990

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