Shallow water wave systems

Clarkson, Peter and Priestley, T.J. (1998) Shallow water wave systems. Studies in Applied Mathematics, 101 (4). pp. 389-432. ISSN 0022-2526. (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)

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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
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: I. Ghose
Date Deposited: 04 Apr 2009 08:10
Last Modified: 14 May 2014 13:59
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