Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation

2022/09/08 by Eychenne, Arnaud, Valet, Frédéric · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.03841

Abstract

We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): ∂_t u + ∂_x (-\vert D \vert^αu + u³)=0. The dipole solution is a solution behaving in large time as a sum of two strongly interacting solitary waves with different signs. We prove the existence of a dipole for fmKdV. A novelty of this article is the construction of accurate profiles. Moreover, to deal with the non-local operator \vert D \vert^α, we refine some weighted commutator estimates.

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