On the standing waves solutions to a nonlocal, nonlinear Schrödinger equation occuring in plasma Physics

Abstract : In this work, our goal is to study the standing waves solutions to some generalization of the following system. iφt + ∆φ = −div(|∇ψ|2∇ψ), ∆ψ = φ. We shall prove the existence of standing waves, solution to this equa- tions and provide some stability results.