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A conservative spectral collocation method for the nonlinear Schrödinger equation in two dimensions

Author

Listed:
  • Zhang, Rongpei
  • Zhu, Jiang
  • Yu, Xijun
  • Li, Mingjun
  • Loula, Abimael F.D.

Abstract

In this study, we present a conservative Fourier spectral collocation (FSC) method to solve the two-dimensional nonlinear Schrödinger (NLS) equation. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. Using the spectral differentiation matrices, the NLS equation is reduced to a system of nonlinear ordinary differential equations (ODEs). The compact implicit integration factor (cIIF) method is later developed for the nonlinear ODEs. In this approach, the storage and CPU cost are significantly reduced such that the use of cIIF method becomes attractive for two-dimensional NLS equation. Numerical results are presented to demonstrate the conservation, accuracy, and efficiency of the method.

Suggested Citation

  • Zhang, Rongpei & Zhu, Jiang & Yu, Xijun & Li, Mingjun & Loula, Abimael F.D., 2017. "A conservative spectral collocation method for the nonlinear Schrödinger equation in two dimensions," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 194-203.
    • Handle: RePEc:eee:apmaco:v:310:y:2017:i:c:p:194-203
    DOI: 10.1016/j.amc.2017.04.035
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    Cited by:

    1. Mohammadi, Reza, 2018. "Smooth Quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 204-215.

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