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Head-on collision between two mKdV solitary waves in a two-layer fluid system

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Abstract

In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdV equation, for short) is investigated by using the reductive perturbation method combined with the PLK method. These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids. The second order perturbation solution is obtained. It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.

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References

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Author notes

  1. Zhu Yong

    Present address: Shanghai Institute of Applied Methematics and Mechanics, Shanghai University of Technology, Shanghai

Authors and Affiliations

  1. Laboratory for Nonlinear Mechanics of Continuous Media, Inst. of Mech., CAS, Beijing

    Zhu Yong

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  1. Zhu Yong
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Communicated by Dai Shi-quiang

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Yong, Z. Head-on collision between two mKdV solitary waves in a two-layer fluid system. Appl Math Mech 13, 407–417 (1992). https://doi.org/10.1007/BF02450731

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  • DOI: https://doi.org/10.1007/BF02450731

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