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

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

doi:10.1088/0305-4470/9/10/002

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

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

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Numerical studies of the regularized long-wave (RLW) equation u _t+u_x+(6u²-u_xt)_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 u_t+u_x+(4u²+2w_xv_t-u _xt)_x=0, with u=w_t=v_x, 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 language	English
Article number	002
Pages (from-to)	L127-L130
Journal	Journal of Physics A: Mathematical and General
Volume	9
Issue number	10
DOIs	https://doi.org/10.1088/0305-4470/9/10/002
Publication status	Published - 1976

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10.1088/0305-4470/9/10/002

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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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year = "1976",

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AU - Gibbon, J. D.

AU - Eilbeck, J. C.

AU - Dodd, R. K.

PY - 1976

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/36149049180

U2 - 10.1088/0305-4470/9/10/002

DO - 10.1088/0305-4470/9/10/002

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 10

M1 - 002

ER -

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

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