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Structure-Preserving Numerical Methods for Fractional Nonlinear Schrödinger Equations with Wave Operators

Author

Listed:
  • Mengnan Zhang

    (College of Science, Jiangnan University, Wuxi 214122, China)

  • Xinyu Zhou

    (College of Science, Jiangnan University, Wuxi 214122, China)

  • Cuicui Liao

    (College of Science, Jiangnan University, Wuxi 214122, China)

Abstract

This main focus of this work is the fractional-order nonlinear Schrödinger equation with wave operators. First, a conservative difference scheme is constructed. Then, the discrete energy and mass conservation formulas are derived and maintained by the difference scheme constructed in this paper. Through rigorous theoretical analysis, it is proved that the constructed difference scheme is unconditionally stable and has second-order precision in both space and time. Due to the completely implicit property of the differential scheme proposed, a linearized iterative algorithm is proposed to implement the conservative differential scheme. Numerical experiments including one example with the fractional boundary conditions were studied. The results effectively demonstrate the long-term numerical behaviors of the fractional nonlinear Schrödinger equations with wave operators.

Suggested Citation

  • Mengnan Zhang & Xinyu Zhou & Cuicui Liao, 2025. "Structure-Preserving Numerical Methods for Fractional Nonlinear Schrödinger Equations with Wave Operators," Mathematics, MDPI, vol. 13(19), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3187-:d:1765131
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    References listed on IDEAS

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    1. Siqi Lv & Zhihua Nie & Cuicui Liao, 2023. "Stability and Convergence Analysis of Multi-Symplectic Variational Integrator for Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 11(17), pages 1-18, September.
    2. Zhang, Xi & Ran, Maohua & Liu, Yang & Zhang, Li, 2023. "A high-order structure-preserving difference scheme for generalized fractional Schrödinger equation with wave operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 532-546.
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