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A series solution of the Cauchy problem for the generalized \(d\)-dimensional Schrödinger equation with a power-law nonlinearity. (English) Zbl 1189.65256

Summary: The Cauchy problem for generalized \(d\)-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.

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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