In this paper, a perturbing nonlinear Schr�dinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods is used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the solution algorithm is tested through computing the only possible first order approximation under truncation procedures. The method of solution is illustrated through case studies and figures.

nonlinear Schr�dinger equation, perturbation, eigenfunction expansion, Mathematica.