Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
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DOI：
10.1016/j.camwa.2015.12.042
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
Siwei Duo;Yanzhi Zhang
中科院分区：
文献类型：
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作者：
Siwei Duo;Yanzhi Zhang
我们提出了三种傅立叶谱方法，即， 分步傅立叶谱（SSFS）、Crank-Nicolson傅立叶谱（CNFS）和松弛傅立叶谱（ReFS）方法，用于求解分数阶非线性薛定谔（NLS）方程。它们都是质量守恒和时间可逆的，空间上具有谱级精度，时间上具有二阶精度。此外，CNFS和ReFS方法是能量守恒的。讨论了这些方法在模拟平面波和孤子动力学中的性能。SSFS方法保持了色散关系，因此它更准确地研究平面波解的长时间行为。此外，我们的数值模拟表明，SSFS方法是更好地解决离焦NLS，但CNFS和ReFS方法是更有效的聚焦NLS。
We propose three Fourier spectral methods, i.e., the split-step Fourier spectral (SSFS), the Crank–Nicolson Fourier spectral (CNFS), and the relaxation Fourier spectral (ReFS) methods, for solving the fractional nonlinear Schrödinger (NLS) equation. All of them are mass conservative and time reversible, and they have the spectral order accuracy in space and the second-order accuracy in time. In addition, the CNFS and ReFS methods are energy conservative. The performance of these methods in simulating the plane wave and soliton dynamics is discussed. The SSFS method preserves the dispersion relation, and thus it is more accurate for studying the long-time behaviors of the plane wave solutions. Furthermore, our numerical simulations suggest that the SSFS method is better in solving the defocusing NLS, but the CNFS and ReFS methods are more effective for the focusing NLS.