Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture

We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schrödinger equation (GNLSE): one is the conservation quantity error adaptive step-control method (RK4IP-CQE), and the other is the local error adaptive step-control method (RK4IP-LEM). Th...

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Bibliographic Details
Published in:Chinese physics B 2023-02, Vol.32 (2), p.24213
Main Authors: Chen, Lei, Li, Pan, Liu, He-Shan, Yu, Jin, Ke, Chang-Jun, Luo, Zi-Ren
Format: Article
Language:English
Subjects:
adaptive step-size methods
coupled-generalized nonlinear Schrödinger equations (C-GNLSE)
nonlinear optics
optical propagation in nonlinear media
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Summary:We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schrödinger equation (GNLSE): one is the conservation quantity error adaptive step-control method (RK4IP-CQE), and the other is the local error adaptive step-control method (RK4IP-LEM). The methods are developed in the vector form of fourth-order Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.
ISSN:1674-1056
DOI:10.1088/1674-1056/ac76a8