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arXiv · 1810.07952

Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

M. Isoard·A. M. Kamchatnov·N. Pavloff
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Abstract

We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

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M. Isoard, A. M. Kamchatnov, N. Pavloff. 2018-10-18. Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method. https://doi.org/10.1103/physreve.99.012210

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