Global well-posedness for the KP-I equation on the background of a non   localized solution
  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). 
Luc Molinet (LAGA), Jean-Claude Saut (LM-Orsay), Nikolay Tzvetkov   (LPP)