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

Luc Molinet·Jean-Claude Saut·Nikolay Tzvetkov
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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).

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Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov. 2006-10-06. Global well-posedness for the KP-I equation on the background of a non localized solution. https://doi.org/10.1007/s00220-007-0243-1

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