Averaging for some periodic and random nonlinear Schrödinger models

In the present communication, we derive averaging equations for nonlinear Schrödinger settings with periodic as well as ergodic random potentials. Our case examples are motivated by recent experimentally accessible applications in soft-condensed matter, as well as in optical physics. Particular features of the resulting equations are compared directly with corresponding predictions of the original model and good agreement is found between the two. Higher order corrections to the leading order averaging results are also discussed.