### 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

Gibbon, J. D., Eilbeck, J. C., & Dodd, R. K. (1976). A modified regularized long-wave equation with an exact two-soliton solution.

*Journal of Physics A: Mathematical and General*,*9*(10), L127-L130. [002]. https://doi.org/10.1088/0305-4470/9/10/002