Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910271076827136 |
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| author | de Brito, L. F. Calazans Gammal, A. Kamchatnov, A. M. |
| author_facet | de Brito, L. F. Calazans Gammal, A. Kamchatnov, A. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05938 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory de Brito, L. F. Calazans Gammal, A. Kamchatnov, A. M. Pattern Formation and Solitons 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. |
| title | Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2601.05938 |