A solitary-wave solution to a perturbed KdV equation
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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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|
|Official Date:||October 2000|
|Page Range:||pp. 475-480|
|Access rights to Published version:||Open Access|
Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413.
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