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Shallow water wave systems

Clarkson, Peter, Priestley, T.J. (1998) Shallow water wave systems. Studies in Applied Mathematics, 101 (4). pp. 389-432. ISSN 0022-2526. (doi:10.1111/1467-9590.00099) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:17649)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1111/1467-9590.00099

Abstract

In this article we study various systems that represent the shallow water wave equation upsilon(xxt) + alpha upsilon upsilon(t) - beta upsilon(x)partial derivative(x)(-1) (upsilon(t)) -upsilon(t) - upsilon(x) = 0, (1) where (partial derivative(x)(-1)f)(x) = integral(x)(infinity)f(y) dy, and alpha and beta are arbitrary, nonzero, constants, The classical method of Lie, the nonclassical method of Bluman and Cole [J. Math. Mech. 18:1025 (1969)], and the direct method of Clarkson and Kruskal [J. Math. Phys. 30:2201 (1989)] are each applied to these systems to obtain their symmetry reductions. It is shown that for both the nonclassical and direct methods unusual phenomena can occur, which leads us to question the relationship between these methods for systems of equations. In particular an example is exhibited in which the direct method obtains a reduction that the nonclassical method does not.

Item Type: Article
DOI/Identification number: 10.1111/1467-9590.00099
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: I. Ghose
Date Deposited: 04 Apr 2009 08:10 UTC
Last Modified: 16 Nov 2021 09:55 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/17649 (The current URI for this page, for reference purposes)

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