Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory

2026/01/09 by L. F. Calazans de Brito, A. Gammal, A. M. Kamchatnov · 1 voice
Physics and Astronomy · #nlin.PS

paper · pdf · doi:10.1103/sh7l-lxck

arxiv published 2026/01/09 · arxiv updated 2026/05/29

Abstract

In this work, we develop, in the Gurevich-Pitaevskii framework, an analytic theory for the evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory for situations when a dispersive shock does not eventually transform into a sequence of well-separated solitons. We found solutions to the Whitham modulation equations for the corresponding so-called "quasi-simple" dispersive shock waves and illustrated this solution with concrete examples of an initial pulse. Comparison of the analytical solution with direct numerical simulations showed that the modulation theory provides a very accurate description of the wave pattern even at one wavelength scale.

Citations

• Linear and nonlinear waves

Discussions

• L. F. Calazans de Brito, A. Gammal, A. M. Kamchatnov: Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory https://arxiv.org/abs/2601.05938 https://arxiv.org/pdf/ [bsky, 0 points, 0 comments]

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