Stability of line solitons for the KP-II equation in ${\mathbb{R}}^2$, II

Abstract

The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi (Mem. Amer. Math. Soc. 238 (2015)) has proved nonlinear stability of $1$-line solitons for exponentially localized perturbations. In this paper, we prove stability of $1$-line solitons for perturbations in $(1+x^2{)}^{-1/2-0}{H}^1({\mathbb{R}}^2)$ and perturbations in $H^1({\mathbb{R}}^2)\cap {\partial }_x{L}^2({\mathbb{R}}^2)$.

48 pages, no figure

References in corpus (4)

• Well-posedness and scattering for the KP-II equation in a critical space
• Global well-posedness for the KP-I equation on the background of a non localized solution
• Remarks on the mass constraint for KP type equations
• Asymptotic stability of solitary waves in the Benney-Luke model of water waves

Cited by in corpus (1)

• Stability of the line soliton of the Kadomtsev--Petviashvili-I equation with the critical traveling speed