This article is cited in 3 papers

Motion of dispersive shock edges in nonlinear pulse evolution

A. M. Kamchatnov

Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, Russia

Abstract: We formulate a method for calculating the velocities of the edges of dispersive shock waves that are generated after wave breaking of pulses during their propagation in a nonlinear medium. The method is based on the properties of the Whitham modulation system at its degenerate limits obtained for either a vanishing amplitude of oscillations at one edge or a vanishing wave number at the other edge.

Keywords: nonlinear wave, soliton, dispersive shock wave, Whitham theory.

PACS: 01.30.Cc, 03.75.Lm, 05.45.Yv

MSC: 35B40, 35C20, 35Q51,35Q55

Received: 28.08.2019
Revised: 28.08.2019

DOI: 10.4213/tmf9800

 English version: Theoretical and Mathematical Physics, 2020, 202:3, 363–370

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