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arXiv · 2110.00100

Trigonometric shock waves for the Kaup-Boussinesq system

Sergey K. Ivanov·Anatoly M. Kamchatnov
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Abstract

We consider the modulationally stable version of the Kaup-Boussinesq system which models propagation of nonlinear waves in various physical systems. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich-Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a non-zero wave excitation on one of the sides of the discontinuity. Our analytical results are confirmed by numerical calculations.

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Sergey K. Ivanov, Anatoly M. Kamchatnov. 2021-09-30. Trigonometric shock waves for the Kaup-Boussinesq system. https://doi.org/10.1007/s11071-022-07326-5

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