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

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 equations and provide some stability results. ∗This work was partially supported by a grant from the Ministère de la Recherche et de la Technologie, France, Contrat no 90S0315. 1 ha l-0 08 48 08 5, v er si on 1 25 J ul 2 01 3 Author manuscript, published in "Physica D: Nonlinear Phenomena 64 (1993) 215-236"