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A solitary-wave solution to a perturbed KdV equation

Published online by Cambridge University Press:  29 May 2001

M. A. ALLEN
Affiliation:
Physics Department, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand
G. ROWLANDS
Affiliation:
Department of Physics, University of Warwick, Coventry CV4 7AL, UK

Extract

We derive the approximate form and speed of a solitary-wave solution to a perturbed KdV equation. Using a conventional perturbation expansion, one can derive a first-order correction to the solitary-wave speed, but at the next order, algebraically secular terms appear, which produce divergences that render the solution unphysical. These terms must be treated by a regrouping procedure developed by us previously. In this way, higher-order corrections to the speed are obtained, along with a form of solution that is bounded in space. For this particular perturbed KdV equation, it is found that there is only one possible solitary wave that has a form similar to the unperturbed soliton solution.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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