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)

Comparison theorems for a generalized modulus of continuity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43943/1/11512_2006_Article_BF02383639.pd