Averaging principle for the Schrödinger equations (Q521488)

The authors deal with the averaging of a class of cubic nonlinear Schrödinger equations, the source of oscillations coming from a rapidly changing potential and a rapidly oscillating forces. The homogenization results are obtained both on finite large time intervals and on the entire time axis. Main ingredients of their proofs include comparison and stability estimates as well as a convergence result between nonlinear Schrödinger equation and its averaged equation. The existence of almost periodic solution for cubic nonlinear Schrödinger equations is also ensured.