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A study on the \(d\)-dimensional Schrödinger equation with a power-law nonlinearity. (English) Zbl 1198.65204
Summary: 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.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q55 NLS equations (nonlinear Schrödinger equations)
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