Existence and stability of standing waves for coupled derivative Schrodinger equations

In this paper, we consider the coupled derivative Schrodinger equations. First, by studying a constrained minimization problem and applying the method of concentration-compactness principle, we obtain the existence of standing waves for the coupled nonlinear derivative Schrodinger equations. Second, we prove that the set of minimizers is a stable set for the initial value problem of the equations in the sense that a solution with initial value starting near the set will remain near it for all time. Finally, we study the structure of the set of minimizers for some special cases. (C) 2015 AIP Publishing LLC.