Standing waves for the nonlinear Schrödinger equation coupled with the Maxwell equation. (4th April 2017) - Colin, Mathieu; Watanabe, Tatsuya
Abstract: In this paper, we are interested in standing waves of the nonlinear Schrödinger equation coupled with the Maxwell equation. Firstly we describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e . Secondly we study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and a link between minimizers and ground states. Finally we study the orbital stability of standing waves for the quadratic nonlinearity.