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INTERACTION OF A SOLITARY WAVE WITH AN EXTERNAL FORCE IN THE EXTENDED KORTEWEG–DE VRIES EQUATION

ROGER GRIMSHAW

Department of Mathematical Sciences, Loughborough University, Loughborough, UK

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and

EFIM PELINOVSKY

Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia

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https://doi.org/10.1142/S0218127402005947Cited by:11 (Source: Crossref)

Abstract

The interaction of a strongly nonlinear solitary wave with an external force is studied using the extended Korteweg–de Vries equation as a model. This equation has several different families of nonlinear wave solutions: solitons, the so-called "thick" solitons, algebraic solitons and breathers, depending upon the sign of the cubic nonlinear term. A simple nonlinear dynamical system of the second order for the amplitude and position of the solitary wave is derived, and used to study the interaction. Its solutions are investigated in the phase plane. The conditions for the capture or reflection of a solitary wave by a single localized external force are obtained, with an emphasis on the role of the cubic nonlinear term.

Keywords:

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