Allen, M. A. and Rowlands, G. (George) (2000) A solitary-wave solution to a perturbed KdV equation. Journal of Plasma Physics, Vol.64 (No.4). pp. 475-480.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Korteweg-de Vries equation, Wave equation -- Numerical solutions, Perturbation (Mathematics), Solitons, Differential equations, Nonlinear
Journal or Publication Title:	Journal of Plasma Physics
Publisher:	Cambridge University Press
ISSN:	0022-3778
Official Date:	October 2000
Dates:	Date Event October 2000 Published
Volume:	Vol.64
Number:	No.4
Page Range:	pp. 475-480
Status:	Peer Reviewed
Access rights to Published version:	Open Access

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