A modified regularized long-wave equation with an exact two-soliton solution

J. D. Gibbon, J. C. Eilbeck, R. K. Dodd

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Abstract

Numerical studies of the regularized long-wave (RLW) equation u t+ux+(6u2-uxt)x=0 suggests it has a two-soliton solution although an analytic form for this has not yet been found. The authors show that a modified form of the RLW equation ut+ux+(4u2+2wxvt-u xt)x=0, with u=wt=vx, has an exact two-soliton solution. The modified equation has the same solitary-wave solution as the original equation and its analytic two-soliton solution agrees closely with the numerical solution of the RLW equation.

Original languageEnglish
Article number002
Pages (from-to)L127-L130
JournalJournal of Physics A: Mathematical and General
Volume9
Issue number10
DOIs
Publication statusPublished - 1976

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planetary waves
wave equations
solitary waves

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abstract = "Numerical studies of the regularized long-wave (RLW) equation u t+ux+(6u2-uxt)x=0 suggests it has a two-soliton solution although an analytic form for this has not yet been found. The authors show that a modified form of the RLW equation ut+ux+(4u2+2wxvt-u xt)x=0, with u=wt=vx, has an exact two-soliton solution. The modified equation has the same solitary-wave solution as the original equation and its analytic two-soliton solution agrees closely with the numerical solution of the RLW equation.",
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A modified regularized long-wave equation with an exact two-soliton solution. / Gibbon, J. D.; Eilbeck, J. C.; Dodd, R. K.

In: Journal of Physics A: Mathematical and General, Vol. 9, No. 10, 002, 1976, p. L127-L130.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Dodd, R. K.

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