Global well-posedness for the KP-I equation on the background of a non localized solution

Abstract

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in $x$ and $y$ periodic or conversely).

Cited by in corpus (2)

• Remarks on the mass constraint for KP type equations
• On the local regularity of the KP-I equation in anisotropic Sobolev space