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

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

2006-10-06

arxiv.org/abs/math/0610223v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00220-007-0243-1

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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