Zeng Liangwei, Shi Jincheng, Belić Milivoj R, Mihalache Dumitru, Chen Junbo, Li Jiawei, Zhu Xing
Opt Express. 2023 Oct 23;31(22):35471-35483. doi: 10.1364/OE.497973.
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 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.
我们证明了在具有五次非线性和周期性线性势的一维非线性薛定谔方程中存在表面间隙孤子，这是一种特殊类型的非对称孤子。非线性在横向空间区域的中间以阶跃状突然切换，而周期性线性势则采用简单的正弦晶格形式。这项工作中的非对称非线性可以通过玻色 - 爱因斯坦凝聚体中的费什巴赫共振或光学中的光折变效应来实现。间隙孤子族中的主要峰值是非对称的，它们位于非线性跳跃的位置（在x = 0处）。此外，在x = 0位置的双峰和多峰孤子的主要峰值高于该位置之后（x>0）的峰值。当化学势的值较大或跳跃处非线性值的差异较大时，这种现象更为明显。在此过程中，对表面间隙孤子进行了线性稳定性分析并确定了稳定域。发现在该模型中，第一带隙中的孤子大多是稳定的（除了带隙边缘的狭窄不稳定域），而第二带隙中的孤子大多是不稳定的（除了基本孤子的极窄稳定域）。这些发现也得到了直接数值模拟的证实。
