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arXiv · 2302.12025

Staggered dispersions: Part I. Shocliton, quantum revival and fractalization

Jian-Zhou Zhu
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Abstract

Alternating the signs of the frequencies for Fourier components with even and odd (normalized) wavenumbers in the nonlinear-wave, such as the Korteweg-de Vries, equations maintains a constantly drifting dispersive shock with similar solitonic oscillations on both sides, like some plasma and quantum shocks. Such \textit{staggered dispersions} support bi-directional waves and can symmetrize and deregularize (to some degree) the nonlinear dynamics, with physical consequences that can also be reflected in the fractalization and quantum revival (Talbot effect).

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Jian-Zhou Zhu. 2023-02-22. Staggered dispersions: Part I. Shocliton, quantum revival and fractalization. https://doi.org/10.1016/j.nls.2025.100050

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