Scattering for the Kadomtsev Petviashili II equation

The KP equations describe two dimensional water waves. The KP-II
equation admits line solitons and it has no localized travelling wave
solution.
The soliton resolution conjecture predicts that solutions with square
integrable
initial data disperse and that the trivial solution is asymptotically
stable
in a suitable sense. We prove that this is the case under a smallness
assumption
in a norm which is critical with respect to scaling.

The proof is based on properties of functions of bounded p-variation
introduced
by Wiener in different context, and on dispersive estimates.