Can I used NDsolve to solve Nonlinear Schroedinger Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation:

 NDSolve[{I D[u[x, t], t] == -0.5*D[u[x, t], x, x] + 0.5*x^2*u[x, t] + 
 Abs[u[x, t]]^2 u[x, t], u[x, 0] == Exp[I*x]}, u, {t, 0, 2}, {x, 0,
 2}]

The above step is not working, I need to get the value of u may be real and imaginary and plot3D for both.

Thanks