Symmetries of a class of nonlinear fourth order partial differential equations

Clarkson, Peter and Priestley, T.J. (1999) Symmetries of a class of nonlinear fourth order partial differential equations. Journal of Nonlinear Mathematical Physics, 6 (1). pp. 66-98. ISSN 1402-9251. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.2991/jnmp.1999.6.1.6

Abstract

In this paper we study symmetry reductions of a class of nonlinear fourth.order partial differential equations u(tt) = (kappa u + gamma u(2))(xx) + uu(xxxx) + mu u(xxtt) + alpha u(x)u(xxx) + beta u(xx)(2), (1) where alpha, beta, gamma, kappa and mu are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a "Boussinesq-type" equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both "compacton" and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are not obtainable through the classical method.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: M. Nasiriavanaki
Date Deposited: 25 Jun 2009 07:27
Last Modified: 14 May 2014 13:59
Resource URI: http://kar.kent.ac.uk/id/eprint/17221 (The current URI for this page, for reference purposes)
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