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

Luc Molinet (1) , Jean-Claude Saut (2) , Nikolay Tzvetkov (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 LPP - Laboratoire Paul Painlevé - UMR 8524

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).

Mots clés: Global existence; Kadomtsev-Petviashvili equation; Non localized solution

Domaines: Equations aux dérivées partielles [math.AP]

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, 2007, 272 (3), pp.775-810. ⟨hal-00104398⟩