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Perturbation theory for approximately integrable partial differential equations, and the change of amplitude of solitary-wave solutions of the BBM equation

Published online by Cambridge University Press:  21 April 2006

J. G. B. Byatt-Smith
J. G. B. Byatt-Smith
Affiliation:
Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK
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Abstract

In this paper we use existing perturbation theories for partial differential equations that are approximately integrable. These methods are then used to study the BBM equations, considered as a perturbation of the KdV equations. We show, analytically, that the amplitudes of two solitary waves are altered after interaction. The change in amplitude is also calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 467 - 483
Copyright
© 1987 Cambridge University Press

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