Dag Nilsson: Existence and decay of lump solutions of the fractional KP equation

Abstract:

The Kadomtsev–Petviashvili equation (KP equation) is a model equation that can be used to describe three-dimensional mainly unidirectional long waves of small amplitude. In this talk I will consider the fractional Kadomtsev–Petviashvili equation (fKP equation), which is a generalization of the classical KP equation involving a fractional derivative. As inte the case of the classical KP-equation, the fKP equation comes in two versions: fKP-I (strong surface tension) and fKP-II (weak surface tension). In the talk I will outline how to prove existence of lump solutions (travelling wave solutions which decay to zero in all horizontal directions) for the fKP-I equation. I will also discuss the smoothness and decay of these lump solutions.

This talk is based on a joint work with Handan Borluk (Ozyegin University) and Gabriele Brüll (Lund University).