Collapse arrest in the space-fractional Schrödinger equation with an optical lattice

doi:10.1088/1674-1056/abefc8

中国物理B ›› 2021, Vol. 30 ›› Issue (10): 104206-104206.doi: 10.1088/1674-1056/abefc8

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

收稿日期:2021-01-04 修回日期:2021-03-11 接受日期:2021-03-18 出版日期:2021-09-17 发布日期:2021-09-17
通讯作者: Hongcheng Wang E-mail:wanghc@dgut.edu.cn
基金资助:
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).

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

Received:2021-01-04 Revised:2021-03-11 Accepted:2021-03-18 Online:2021-09-17 Published:2021-09-17
Contact: Hongcheng Wang E-mail:wanghc@dgut.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: soliton solution, collapse, variational approach, nonlinear Schrödinger equation

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.

Key words: soliton solution, collapse, variational approach, nonlinear Schrödinger equation

中图分类号: (Optical solitons; nonlinear guided waves)

42.65.Tg

42.65.Jx (Beam trapping, self-focusing and defocusing; self-phase modulation) 42.25.Bs (Wave propagation, transmission and absorption)

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[J]. 中国物理B, 2021, 30(10): 104206-104206.

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Collapse arrest in the space-fractional Schrödinger equation with an optical lattice

Collapse arrest in the space-fractional Schrödinger equation with an optical lattice

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