Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory
Pattern Formation and Solitons
2026-01-12 v1
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.
Keywords
Cite
@article{arxiv.2601.05938,
title = {Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory},
author = {L. F. Calazans de Brito and A. Gammal and A. M. Kamchatnov},
journal= {arXiv preprint arXiv:2601.05938},
year = {2026}
}
Comments
10 pages, 5 figures