AI 中文总结
研究二维光学系统中准一维连续波，借助立方-五次非线性和一维势阱，确认特定横向结构连续波的调制不稳定性，生成二维孤子周期链稳态并研究其动力学，还找到奇异势阱下连续波的精确解析解。
AI 中文摘要
我们考虑具有立方-五次非线性和一维势阱的二维光学系统中的准一维连续波。对于平滑的势阱轮廓，我们确认了具有对应于势阱中一维基态横向结构的准一维连续波的已知调制不稳定性，并证明了具有对应于势阱中最低一维激发态的偶极模横向结构的连续波的调制不稳定性。基态和偶极模类型的连续波在其存在区域边缘附近几乎保持稳定。以数值形式产生了被困在势阱中的二维孤子周期链形式的稳定稳态。还研究了由局部脉冲激发的孤子链的动力学。对于具有奇异δ函数轮廓的势阱，我们找到了两种连续波的精确解析解，其中一种是完全稳定的。
英文摘要
We consider quasi-one-dimensional (Q1D) continuous waves (CWs) in the two-dimensional (2D) optical system with the cubic-quintic nonlinearity and a Q1D potential trough. In the case of a smooth trough profile, we confirm the known modulational instability (MI) of Q1D CWs with the transverse structure corresponding to the 1D ground state (GS) in the potential trough, and demonstrate the MI of CWs with the dipole-mode (DM) transverse structure, corresponding to the lowest 1D excited state in the potential trough. The CWs of both GS and DM types remain nearly stable close to the edges of their existence regions. Stable stationary states in the form of periodic chains of 2D solitons, trapped in the potential trough, are produced in a numerical form. The dynamics of the soliton chains excited by a localized kick is studied too. For the potential trough with the singular delta-functional profile, we find two species of exact analytical solutions for CWs, one of which is completely stable.
Commentsto be published in Photonics (MDPI), a special issue "New Perspectives in Laser Nonlinearity: Phenomena, Theory, and Breakthroughs"
