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Discontinuities of the variables that characterize the propagation of solitary waves in a fluid layer

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Abstract

A nonlinear system of equations of hyperbolic type describing the propagation of solitary waves is considered [1]. A solitary wave is characterized in this approximation by two variables — the energy density per unit length measured along its crest, and the direction of the normal to the wave crest. The evolution of a wave described by the system may lead to the appearance of discontinuities, at which there are jumps in the energy density and the direction of the wave crest [2]. To establish the conditions at the discontinuities, a solution describing the interaction of nonparallel solitons [3, 4] is used. The obtained conditions are used to solve the problem of the decay of an arbitrary discontinuity in terms of soliton variables.

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Literature cited

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Authors and Affiliations

  1. Moscow

    I. B. Bakholdin

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  1. I. B. Bakholdin
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 87–93, May–June, 1984.

I thank A. G. Kulikovskii and A. A. Barmin for helpful discussions and valuable comments in the preparation of the paper.

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Bakholdin, I.B. Discontinuities of the variables that characterize the propagation of solitary waves in a fluid layer. Fluid Dyn 19, 416–422 (1984). https://doi.org/10.1007/BF01093906

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  • DOI: https://doi.org/10.1007/BF01093906

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