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

Tingxiao He, Yun Wang and Yingnan Zhang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 630-639

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.

Keywords: Derivative nonlinear Schrödinger equation; Integrable discretization; Fourier Pseudo-spectral method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:630-639

DOI: 10.1016/j.matcom.2024.02.020

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