Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2

Abstract

In this paper, we study the existence and the properties of standing waves of the form $u_{\omega}(x,t)=\phi_{\omega}(x)e^{i\omega t},$ where $ x\in \mathbb R^2,$ $t\geq 0$, for a quasilinear Schrödinger equation. Using the minimization method introduced by T. Cazenave and P.L. Lions, we prove a stability theorem for such waves.