A random dispersion Schrodinger equation with time-oscillating nonlinearity

In this paper, we consider the nonlinear Schrodinger equation with the random dispersion and time-oscillating nonlinearity, iut + 1/epsilon m (t/epsilon(2))partial derivative xx u + theta(t/epsilon(2)) vertical bar u vertical bar(2 sigma) u=0, x epsilon R, t > 0, sigma > 0, where m satisfying some ergodic conditions and theta a periodic function. We prove that the solution u(epsilon) converges as epsilon -> 0 to the solution of the limit equation idu+ partial derivative xx u o d beta + I (theta)vertical bar u vertical bar(2 sigma) udt =0 with the initial datum u(0) in H-1 (R). And the convergence holds in the sense of distribution in C([0, T]; H-1 (R)), T < T*(u(0)) almost surely, where T*(u(o)) is the maximal existence time for the limit equation. (C) 2014 Elsevier Inc. All rights reserved.