## 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.
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### 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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### References:

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