Self-similar solutions for the generalized fractional Korteweg-de Vries equation

2024/10/15 by Molinet, Luc, Vento, Stéphane, Weissler, Fred · 1 citation
#35C06 #35Q35 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.12063

Abstract

We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation u_t+D^αu_x + u^p u_x= 0, 1lt;α≤ 2, p∈ \mathbb N∖\0\, with homogeneous initial data Φ. We show that, under smallness assumption on Φ, and for a wide range of (α, p), including p=3, we can construct a self-similar solution of this problem.

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• Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation

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