Decay of solitary waves of fractional Korteweg-de Vries type equations

2022/10/14 by Eychenne, Arnaud, Valet, Frédéric · 1 citation
#35R11 #35S30 #76B25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35C20 #Secondary: 35Q35

paper · doi:10.48550/arxiv.2210.07966

Abstract

We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the 1-dimensional semi-linear fractional equations: \vert D \vert^αu + u -f(u)=0, with α∈ (0,2), a prescribed coefficient p^*(α), and a non-linearity f(u)=\vert u \vert^p-1u for p∈(1,p^*(α)), or f(u)=u^p with an integer p∈[2;p^*(α)). Asymptotic developments of order 1 at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion α and of the non-linearity p. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory.

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