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

Abstract

Motivated by transverse stability issues, we address the time evolution under the KP-II flow of perturbations of a solution which does not decay in all directions, for instance the KdV-line soliton. We study two different types of perturbations : perturbations that are square integrable in $ \R\times \T $ and perturbations that are square integrable in ${\mathbb{R}}^2$. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.

References in corpus (4)

• Well-posedness and scattering for the KP-II equation in a critical space
• Global well-posedness of the KP-I initial-value problem in the energy space
• Global well-posedness for the KP-I equation on the background of a non localized solution
• On KP-II type equations on cylinders

Cited by in corpus (5)

• Modulation theory for soliton resonance and Mach reflection
• Justification of the KP-II approximation in dynamics of two-dimensional FPU systems
• The direct scattering problem for perturbed Kadomtsev-Petviashvili multi line solitons
• The direct scattering problem for the perturbed $\text{Gr}(1,2{)}_{\ge 0}$ Kadomtsev-Petviashvili solitons
• Existence of solutions for the surface electromigration equation