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A solitary-wave solution to a perturbed KdV equation

By M. A. Allen and G. (George) Rowlands


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

Topics: QA
Publisher: Cambridge University Press
Year: 2000
OAI identifier: oai:wrap.warwick.ac.uk:837

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