Stability and instability results for standing waves of quasi-linear Schrödinger equations

We study a class of quasi-linear Schrödinger equations arising in the theory of superfluid film in plasma physics. Using gauge transforms and a derivation process we solve, under some regularity assumptions, the Cauchy problem. Then, by means of variational methods, we study the existence, the orbital stability and instability of standing waves which minimize some associated energy.