Nonlinear Cubic Homogeneous Schrodinger Equations with Complex Initial Conditions, Limited Time Response

Abstract: In this paper, a perturbing nonlinear homogeneous Schrodinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation and Picard approximation methods together with the eigenfunction 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.