Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture
Lei Chen(陈磊)1,3, Pan Li(李磐)2,3,†, He-Shan Liu(刘河山)2,3, Jin Yu(余锦)1,3, Chang-Jun Ke(柯常军)1,3, and Zi-Ren Luo(罗子人)2,3,‡
1 Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China; 2 National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 3 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract 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.
Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104).
Corresponding Authors:
Pan Li, Zi-Ren Luo
E-mail: lipan@imech.ac.cn;luoziren@imech.ac.cn
Cite this article:
Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人) Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture 2023 Chin. Phys. B 32 024213
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