Symmetries of a class of nonlinear third-order partial differential equations

Clarkson, Peter and Mansfield, Elizabeth L. and Priestley, T.J. (1997) Symmetries of a class of nonlinear third-order partial differential equations. Mathematical and Computer Modelling, 25 (8-9). pp. 195-212. ISSN 0895-7177. (The full text of this publication is not available from this repository)

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Abstract

In this paper, we study symmetry reductions of a class of nonlinear third-order partial differential equations (1) U-t - epsilon u(xxt) + 2 kappa u(x) = uu(xxx) + alpha uu(x) + beta u(x)u(xx), where epsilon, kappa, alpha, and beta are arbitrary constants. Three special cases of equation (1) have appeared in the literature, up to some rescalings. In each case, the equation has admitted unusual travelling wave solutions: the Fornberg-Whitham equation, for the parameters epsilon = 1, alpha = -1, beta = 3, and kappa = 1/2, admits a wave of greatest height, as a peaked limiting form of the travelling wave solution; the Rosenau-Hyman equation, for the parameters epsilon = 0, alpha = 1, beta = 3, and kappa = 0, admits a ''compacton'' solitary wave solution; and the Fuchssteiner-Fokas-Camassa-Holm equation,for the parameters epsilon = 1, alpha = -3, and beta = 2, has a ''peakon'' solitary wave solution. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole.

Item Type: Article
Uncontrolled keywords: Camassa-Holm equation; group-invariant solution; nonclassical method; symmetry reduction
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: T. Nasir
Date Deposited: 25 Oct 2009 11:01
Last Modified: 14 May 2014 14:00
Resource URI: http://kar.kent.ac.uk/id/eprint/18356 (The current URI for this page, for reference purposes)
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