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

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  • Shidfar, A.
  • Molabahrami, A.
  • Babaei, A.
  • Yazdanian, A.

Abstract

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.

Suggested Citation

  • Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2154-2158
    DOI: 10.1016/j.chaos.2009.03.139
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    References listed on IDEAS

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    1. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
    2. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    3. Zhu, Shun-dong, 2007. "Exact solutions for the high-order dispersive cubic-quintic nonlinear Schrödinger equation by the extended hyperbolic auxiliary equation method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1608-1612.
    4. Wazwaz, Abdul-Majid, 2008. "A study on linear and nonlinear Schrodinger equations by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1136-1142.
    5. Abdou, M.A., 2008. "New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 949-955.
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