Affiliation:
1. Guangzhou Maritime University
2. Shenzhen University
3. 54th Research Institute of CETC
4. Texas A&M University at Qatar
5. Horia Hulubei National Institute of Physics and Nuclear Engineering
6. Jiaying University
7. Xi’an Jiaotong University
Abstract
We demonstrate the existence of surface gap solitons, a special type of asymmetric solitons, in the one-dimensional nonlinear Schrödinger equation with quintic nonlinearity and a periodic linear potential. The nonlinearity is suddenly switched in a step-like fashion in the middle of the transverse spatial region, while the periodic linear potential is chosen in the form of a simple sin 2 lattice. The asymmetric nonlinearities in this work can be realized by the Feshbach resonance in Bose-Einstein condensates or by the photorefractive effect in optics. The major peaks in the gap soliton families are asymmetric and they are located at the position of the jump in nonlinearity (at x = 0). In addition, the major peaks of the two-peak and multi-peak solitons at the position x = 0 are higher than those after that position, at x > 0. And such phenomena are more obvious when the value of chemical potential is large, or when the difference of nonlinearity values across the jump is big. Along the way, linear stability analysis of the surface gap solitons is performed and the stability domains are identified. It is found that in this model, the solitons in the first band gap are mostly stable (excepting narrow domains of instability at the edges of the gap), while those in the second band gap are mostly unstable (excepting extremely narrow domains of stability for fundamental solitons). These findings are also corroborated by direct numerical simulations.
Funder
National Natural Science Foundation of China
Guangdong Basic and Applied Basic Research Foundation
Guangdong Province Education Department Foundation of China
Meizhou City Social Development Science and Technology Plan Project
Romanian Ministry of Research, Innovation, and Digitization
Qatar National Research Fund
Subject
Atomic and Molecular Physics, and Optics