Existence of solitary wave solutions for the full dispersion Kadomtsev-Petviashvili equation

Speaker: Dag Nilsson (Lund University)

Abstract:

The full dispersion Kadomtsev–Petviashvili (FDKP) equation is a model equation describing three-dimensional long waves of small amplitude. The FDKP equation is a fully dispersive version of the classical KP equation, similar to how the Whitham equation is a fully dispersive version of the KdV equation. In my talk I will consider the weak surface tension regime and describe how to prove existence of solitary wave solutions for the FDKP-equation. The proof is variational and relies upon a series of reductive steps which transform the FDKP-functional to a perturbed scaling of the Davey–Stewartson functional, for which solitary waves are found.

This talk is based on a joint work with Mats Ehrnström (NTNU) and Mark Groves (Saarland University).