A numerical and symbolical approximation of the nonlinear Anderson model

A modified perturbation theory, with regard to the strength of the nonlinear term, is developed to solve the nonlinear Schrödinger equation with a random potential. It is demonstrated that in some cases it is substantially more efficient than other methods. Moreover, we obtain error estimates that are explicitly computable within the theory. This approach can be useful for the solution of other nonlinear differential equations of physical relevance.