A series solution of the Cauchy problem for the generalized d-dimensional Schroedinger equation with a power-law nonlinearity

摘要

In this paper, the Cauchy problem for generalized d-dimensional Schrodinger equation with a power-law nonlinearity is studied. Three methods, homotopy analysis method (HAM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM), are applied to obtain series pattern solutions of the mentioned Cauchy problem. The recurrent relations, for solving the mentioned Cauchy problem, is introduced. For some cases of given initial conditions, we obtain the closed form of the exact solutions.