### Abstract

Numerical studies of the regularized long-wave (RLW) equation u _{t}+u_{x}+(6u^{2}-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}+(4u^{2}+2w_{x}v_{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 |
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Article number | 002 |

Pages (from-to) | L127-L130 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 9 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1976 |

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### Cite this

*Journal of Physics A: Mathematical and General*,

*9*(10), L127-L130. [002]. https://doi.org/10.1088/0305-4470/9/10/002

}

*Journal of Physics A: Mathematical and General*, vol. 9, no. 10, 002, pp. L127-L130. https://doi.org/10.1088/0305-4470/9/10/002

**A modified regularized long-wave equation with an exact two-soliton solution.** / Gibbon, J. D.; Eilbeck, J. C.; Dodd, R. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A modified regularized long-wave equation with an exact two-soliton solution

AU - Gibbon, J. D.

AU - Eilbeck, J. C.

AU - Dodd, R. K.

PY - 1976

Y1 - 1976

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 - http://www.scopus.com/inward/record.url?scp=36149049180&partnerID=8YFLogxK

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

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

M3 - Article

VL - 9

SP - L127-L130

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 10

M1 - 002

ER -