Collision of two solitary waves for the Zakharov-Kuznetsov equation (Frédéric Valet, CY Cergy Paris Université)Séminaire « Analyse numérique et équations aux dérivées partielles »
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 phe-
nomena 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.