Séminaire d'analyse

Stability of two solitary waves for the Zakharov-Kuznetsov equation

by Dr Frédéric Valet

E2290 (Tours)




The Zakharov-Kuznetsov equation is a dispersive PDE that generalizes the Korteweg-de Vries equation in
dimension larger than one in plasma physics. It admits solitary waves, that are solutions keeping their form
along the time, moving at a constant speed in one direction. A natural question is the stability of those solitary
waves : if an initial condition is close to a solitary wave, what is the long time behaviour of the solution? In
this talk we will recall the results and the tools to prove orbital stability of one solitary wave and multi-solitary
waves and then recall the proof of the asymptotic stability of one solitary wave. We then detail the new result
of asymptotic stability of two solitary waves. The talk is based on a joint work with Didier Pilod (Universitet i

Organized by

Vincent Perrollaz