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

2006/10/06 by Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov · 1 citation
Mathematics · #math.AP #msc:35Q53 #msc:35Q51 #msc:35A05

paper · pdf · doi:10.1007/s00220-007-0243-1

arxiv created 2006/10/06 · arxiv updated 2009/12/01

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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