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

Molinet, Luc; Saut, Jean-Claude; Tzvetkov, Nikolay

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 653-676.

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 ${ℝ}^2$. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.

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