High-order schemes for the fractional coupled nonlinear Schrödinger equation

Fengli Yin; Dongliang Xu; Wenjie Yang; Fengli Yin; Dongliang Xu; Wenjie Yang

doi:10.3934/nhm.2023063

Networks and Heterogeneous Media

2023, Volume 18, Issue 4: 1434-1453. doi: 10.3934/nhm.2023063

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Research article

High-order schemes for the fractional coupled nonlinear Schrödinger equation

1.
Zhoukou Normal University, Zhoukou 466000, China
2.
Nanjing University of Finance and Economics Hongshan College, Nanjing 210023, China
3.
School of Science, Xuchang University, Xuchang 461000, China

Received: 14 March 2023 Revised: 19 May 2023 Accepted: 31 May 2023 Published: 15 June 2023

This paper considers the fractional coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the quadratic auxiliary variable method. To this end, we develop the multiple quadratic auxiliary variable approach and then construct a family of structure-preserving schemes with the help of the symplectic Runge-Kutta method for solving the equation. The given schemes have high accuracy in time and can both inherit the mass and Hamiltonian energy of the system. Ample numerical results are given to confirm the accuracy and conservation of the developed schemes at last.
- multiple quadratic auxiliary variable,
- fractional coupled Schrödinger equation,
- conservative schemes,
- high-accuracy,
- numerical stability
Citation: Fengli Yin, Dongliang Xu, Wenjie Yang. High-order schemes for the fractional coupled nonlinear Schrödinger equation[J]. Networks and Heterogeneous Media, 2023, 18(4): 1434-1453. doi: 10.3934/nhm.2023063

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Abstract

This paper considers the fractional coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the quadratic auxiliary variable method. To this end, we develop the multiple quadratic auxiliary variable approach and then construct a family of structure-preserving schemes with the help of the symplectic Runge-Kutta method for solving the equation. The given schemes have high accuracy in time and can both inherit the mass and Hamiltonian energy of the system. Ample numerical results are given to confirm the accuracy and conservation of the developed schemes at last.

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