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

In this paper, the Cauchy problem for generalized dd-dimensional Schrödinger 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.