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arXiv · 2601.05938

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

L. F. Calazans de Brito·A. Gammal·A. M. Kamchatnov
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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.

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L. F. Calazans de Brito, A. Gammal, A. M. Kamchatnov. 2026-01-09. Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory. https://arxiv.org/abs/2601.05938

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