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A partial-integrable numerical simulation scheme of the derivative nonlinear Schrödinger equation

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  • He, Tingxiao
  • Wang, Yun
  • Zhang, Yingnan

Abstract

In this paper, we present a novel approach for discretizing the derivative Nonlinear Schrödinger (DNLS) equation in an integrable manner. Our proposed method involves discretizing the time variable, resulting in a discrete system that converges to the DNLS equation in a natural limit. Furthermore, the discrete system retains the same set of infinitely conserved quantities as the original DNLS equation. To demonstrate the effectiveness of our proposed method, we designed a numerical simulation scheme using the Fourier Pseudo-spectral Method to discretize the spatial variable. The numerical results confirm that our new discrete integrable scheme can accurately preserve the conserved quantities of the DNLS equation.

Suggested Citation

  • He, Tingxiao & Wang, Yun & Zhang, Yingnan, 2024. "A partial-integrable numerical simulation scheme of the derivative nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 630-639.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:630-639
    DOI: 10.1016/j.matcom.2024.02.020
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    References listed on IDEAS

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    1. Li, Meng & Zhao, Yong-Liang, 2018. "A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 758-773.
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