A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces

Abstract

In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^s(\mathbb{R})\cap L^2(|x{|}^{2r}dx)$ for $s=1/12+\epsilon$ and any $r\in (0,R)$, for some $0<\epsilon <1/4$ and $0<R<s/2$.

22 pages

References in corpus (1)

• The Nonlinear Schrödinger-Airy equation in weighted Sobolev spaces