Collapse arrest in the space-fractional Schrödinger equation with an optical lattice
Manna Chen(陈曼娜)1, Hongcheng Wang(王红成)1,†, Hai Ye(叶海)1, Xiaoyuan Huang(黄晓园)1, Ye Liu(刘晔)1, Sumei Hu(胡素梅)2, and Wei Hu(胡巍)3
1 School of Electrical Engineering and Intelligentization, Dongguan University of Technology, Dongguan 523808, China; 2 Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000, China; 3 Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006, China
Abstract The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrödinger equation with Kerr nonlinearity and optical lattice. The approximate analytical soliton solutions are obtained based on the variational approach, which provides reasonable accuracy. Linear-stability analysis shows that all the solitons are linearly stable. No collapses are found when the Lévy index 1<α≤2. For α=1, the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough. It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrödinger equation still holds in the one-dimensional fractional Schrödinger equation. The physical mechanism for collapse prohibition is also given.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11947122), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515110935), the Research Start-up Foundation of Dongguan University of Technology, the Guangdong Science and Technology Planning Program (Grant No. 2017A010102019), the Guangdong Province Natural Science Foundation of China (Grant Nos. 2018A030307028 and 2019A1515010916), and the Maoming Natural Science Foundation of Guangdong, China (Grant No. 2019018001).
Corresponding Authors:
Hongcheng Wang
E-mail: wanghc@dgut.edu.cn
Cite this article:
Manna Chen(陈曼娜), Hongcheng Wang(王红成), Hai Ye(叶海), Xiaoyuan Huang(黄晓园), Ye Liu(刘晔), Sumei Hu(胡素梅), and Wei Hu(胡巍) Collapse arrest in the space-fractional Schrödinger equation with an optical lattice 2021 Chin. Phys. B 30 104206
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