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NON DISPERSIVE SOLUTIONS OF THE GENERALIZED KDV EQUATIONS ARE TYPICALLY MULTI-SOLITONS

Abstract : We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense (in the spirit of [18]) and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non-dispersion.
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https://hal.archives-ouvertes.fr/hal-02888404
Contributor : Xavier Friederich <>
Submitted on : Friday, July 3, 2020 - 8:26:30 AM
Last modification on : Monday, July 6, 2020 - 11:51:12 AM

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  • HAL Id : hal-02888404, version 1
  • ARXIV : 2007.01577

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Xavier Friederich. NON DISPERSIVE SOLUTIONS OF THE GENERALIZED KDV EQUATIONS ARE TYPICALLY MULTI-SOLITONS. 2020. ⟨hal-02888404⟩

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