On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation

In this paper, a perturbing nonlinear cubic non-homogeneous Schrodinger equation, i partial derivative u(t, z)/partial derivative z + alpha (partial derivative boolean AND 2 u(t, z))/(partial derivative t boolean AND 2) + epsilon vertical bar u(t, z)vertical bar boolean AND 2 u(t, z) + i gamma u(t, z) = F_1 (t, z) + i F_2 (t, z), (t, z) is an element of (0, T) x (0, infinity) is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation method and Picard approximation together with the eigen function expansion and variational parameters methods are 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 possible orders of approximations. The method of solution is illustrated through case studies and figures. Effect of time interval (T) had been studied through cases studies and figures.