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

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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.