In this paper, we consider the nonlinear Schrödinger equation with the random dispersion and time-oscillating nonlinearity,
where
m satisfying some ergodic conditions and
胃 a periodic function. We prove that the solution
u蔚 converges as
蔚→0 to the solution of the limit equation
with the initial datum
u0 in
H1(R). And the convergence holds in the sense of distribution in
C([0,T];H1(R)),
T<蟿鈦?/sup>(u0) almost surely, where
蟿鈦?/sup>(u0) is the maximal existence time for the limit equation.