Orbital stability of optical solitons in 2D

We present a stability result for groundstates of a Schrödinger–Poisson system in dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. The core of the proof is a coercivity bound on the second derivative of the action, where non scaling nonlinearities and the coupled system present the major difficulties. In addition we prove existence of a ground state with frequency σ for any as a minimal point over an appropriate Nehari manifold.