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×T and perturbations that are square integrable in R2. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.
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