Zhu Xing, Fan Yan, Belić Milivoj R, Mihalache Dumitru, Xiang Dan, Zeng Liangwei
Opt Express. 2025 Feb 24;33(4):7205-7217. doi: 10.1364/OE.553947.
In this work, we establish the existence of different dark soliton families in the nonlinear Schrödinger equation with purely cubic-quintic nonlinear lattices, including individual dark solitons and soliton clusters with varying numbers of valleys. We explore two types of cubic-quintic lattices, the competing lattices (with the nonlinear terms of opposite signs) and the defocusing lattices (with the nonlinear terms of the same signs). The spacing between the valleys of dark soliton clusters is chosen as an integer multiple of the lattice's period. We find that the stability domains of dark solitons in the defocusing lattices are larger than those in the competing lattices. The stability domains of dark soliton families are obtained by linear stability analysis and confirmed by direct numerical simulations. Both stable and unstable propagations of such families are displayed, highlighting the distinct dynamics introduced by these nonlinear interactions and their impact on the formation and stability of dark solitons.
在这项工作中，我们在具有纯三次 - 五次非线性晶格的非线性薛定谔方程中建立了不同暗孤子族的存在性，包括单个暗孤子和具有不同谷数量的孤子簇。我们研究了两种类型的三次 - 五次晶格，即竞争晶格（非线性项符号相反）和散焦晶格（非线性项符号相同）。暗孤子簇谷之间的间距被选为晶格周期的整数倍。我们发现散焦晶格中暗孤子的稳定域比竞争晶格中的稳定域大。暗孤子族的稳定域通过线性稳定性分析获得，并通过直接数值模拟得到证实。展示了此类族的稳定和不稳定传播，突出了这些非线性相互作用引入的独特动力学及其对暗孤子形成和稳定性的影响。
