The Zakharov-Kuznetsov (ZK) equation in dimension 2 is a generalization in plasma physics of the one-dimensional Korteweg de Vries equation (KdV). Both equations admit solitary waves, that are solutions moving in one direction at a constant velocity, vanishing at infinity in space. When two solitary waves collide, two phenomena can occur: either the structure of two solitary waves is conserved without any loss of energy and change of sizes (elastic collision), or the structure is lost or modified (inelastic collision). As a completely integrable equation, KdV only admits elastic collisions. The goal of this talk is to explain the collision phenomenon for two solitary waves having almost the same size for ZK. The talk is based on a collaboration with Didier Pilod.
Romain Duboscq, David Lafontaine