Publication: A solitary-wave solution to a perturbed KdV equation
Issued Date
2000-01-01
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ISSN
00223778
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2-s2.0-0034289236
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Mahidol University
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SCOPUS
Bibliographic Citation
Journal of Plasma Physics. Vol.64, No.4 (2000), 475-480
Suggested Citation
M. A. Allen, G. Rowlands A solitary-wave solution to a perturbed KdV equation. Journal of Plasma Physics. Vol.64, No.4 (2000), 475-480. doi:10.1017/S0022377800008813 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/26367
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Title
A solitary-wave solution to a perturbed KdV equation
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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.