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A solitary-wave solution to a perturbed KdV equation

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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. ISSN 0022-3778

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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
Date:	October 2000
Volume:	Vol.64
Number:	No.4
Page Range:	pp. 475-480
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413. Chang, H.-Y., Raychaudhuri, S., Hill, J., Tsikis, E. K. and Longrenn, K. E. 1986 Phys. Fluids 29, 294. Gardner, C. S., Greene, J. M., Kruskal, M. D. and Miura, R. M. 1967 Phys. Rev. Lett. 19, 1095. Infeld, E. and Rowlands, G. 2000 Nonlinear Waves, Solitons and Chaos, 2nd edn. Cambridge University Press. Karpman, V. I. and Maslov, E. M. 1978 Zh. Eksp. Teor. Fiz. 75, 504 [Soviet Phys. JETP 48, 252 (1978)]. Kivshar, Y. S. and Malomed, B. A. 1989 Rev. Mod. Phys. 61, 763. Rowlands, G. 1969 J. Plasma Phys. 3, 567. Wolfram, S. 1991 Mathematica. Addison-Wesley, Reading, MA.
URI:	http://wrap.warwick.ac.uk/id/eprint/837