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arXiv · 1010.3996

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

Luc Molinet·Jean-Claude Saut·Nikolay Tzvetkov
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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 $ \R^2 $. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.

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Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov. 2010-10-19. Global well-posedness for the KP-II equation on the background of a non localized solution. https://doi.org/10.1016/j.anihpc.2011.04.004

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