Non dispersive solutions of the generalized KdV equations are typically multi-solitons

2020/07/03 by Xavier Friederich, Friederich, Xavier
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2007.01577

openalex publication_date 2020/07/03 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28

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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