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Analysis of the damped nonlinear space-fractional Schrödinger equation

Author

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  • Liang, Jiarui
  • Song, Songhe
  • Zhou, Weien
  • Fu, Hao

Abstract

In this paper, we verify the unique existence of the global smooth solution of the damped nonlinear space-fractional Schrödinger (DNFS) equation and show it follows a conformal mass conservation law. We propose a conformal mass-preserving linearized scheme. It is rigorously proved that this scheme preserves the discrete conformal mass. Furthermore, we prove that the proposed scheme admits a unique solution and is of second order convergence in space and first order convergence in time. Some numerical experiments are carried out to validate the theoretical analysis.

Suggested Citation

  • Liang, Jiarui & Song, Songhe & Zhou, Weien & Fu, Hao, 2018. "Analysis of the damped nonlinear space-fractional Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 495-511.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:495-511
    DOI: 10.1016/j.amc.2017.10.010
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
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    Cited by:

    1. Fu, Yayun & Song, Yongzhong & Wang, Yushun, 2019. "Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 206-223.

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