A study on the d-dimensional Schrödinger equation with a power-law nonlinearity

In this paper, the homotopy perturbation method (HPM) is applied to obtain series pattern solutions of the Cauchy problem for the d-dimensional Schrödinger equation with a power-law nonlinearity. We introduce the recurrent relation to solve the mentioned Cauchy problem. For some cases of given initial condition, we obtain the closed form of the exact solutions.