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

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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Submitted on : Friday, October 6, 2006 - 2:38:27 PM
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Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov. Global well-posedness for the KP-I equation on the background of a non localized solution. Communications in Mathematical Physics, Springer Verlag, 2007, 272 (3), pp.775-810. ⟨hal-00104398⟩

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