Asymptotic N-soliton-like solutions of the fractional Korteweg-de Vries equation

2021/12/21 by Eychenne, Arnaud · 2 citations
#35Q35 Secondary: 35B40 #37K40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35Q53

paper · doi:10.48550/arxiv.2112.11278

Abstract

We construct N-soliton solutions for the fractional Korteweg-de Vries (fKdV) equation ∂_t u - ∂_x(|D|^αu - u² )=0, in the whole sub-critical range α∈]\frac12,2[. More precisely, if Q_c denotes the ground state solution associated to fKdV evolving with velocity c, then given 0

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