## Séminaire d'analyse

**Stability of two solitary waves for the Zakharov-Kuznetsov equation**

Frédéric Valet

Thursday 23 November 2023 14:00 - Tours - E2290

**Résumé :**

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

Bergen).

**Liens :**