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Local structure-preserving algorithms for the nonlinear Schrödinger equation with power law nonlinearity

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  • Luo, Fangwen
  • Tang, Qiong
  • Huang, Yiting
  • Ding, Yanhui
  • Tang, Sijia

Abstract

This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schrödinger equation with power law nonlinearity, comprising two local energy-conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algorithms to achieve global conservation under periodic boundary conditions. Theoretical analyses confirm the conservation properties of these algorithms. In numerical experiments, we validate the advantages of these algorithms in maintaining long-term energy or momentum conservation by comparing them with a multi-symplectic Preissman algorithm.

Suggested Citation

  • Luo, Fangwen & Tang, Qiong & Huang, Yiting & Ding, Yanhui & Tang, Sijia, 2025. "Local structure-preserving algorithms for the nonlinear Schrödinger equation with power law nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 484(C).
    • Handle: RePEc:eee:apmaco:v:484:y:2025:i:c:s0096300324004478
    DOI: 10.1016/j.amc.2024.128986
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    References listed on IDEAS

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    1. Barletti, L. & Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2018. "Energy-conserving methods for the nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 3-18.
    2. Frasca-Caccia, Gianluca & Hydon, Peter E., 2021. "Numerical preservation of multiple local conservation laws," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Li, Haochen & Jiang, Chaolong & Lv, Zhongquan, 2018. "A Galerkin energy-preserving method for two dimensional nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 16-27.
    4. Langyang Huang & Zhaowei Tian & Yaoxiong Cai, 2020. "Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, January.
    5. Fu, Yayun & Hu, Dongdong & Wang, Yushun, 2021. "High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 238-255.
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