School of Physics and Electrical Engineering, Liupanshui Normal University, Liupanshui 553004, China.
Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan.
Chaos. 2022 Dec;32(12):123105. doi: 10.1063/5.0106915.
We study the relationship between the structures of the nonlinear localized waves and the distribution characteristics of the modulation stability regime in a nonlinear fiber with both third-order and fourth-order effects. On the background frequency and background amplitude plane, the modulation stability region consists of two symmetric curves on the left and right and a point on the symmetry axis. We find that the higher-order excitation characteristics are obviously different at different positions in the modulation stability region. Their excitation characteristics are closely related to the modulation instability distribution characteristics of the system. It is shown that asymmetric high-order rational solitons are excited at the left and right stable curves, and the symmetric one is excited at the stable points. Interestingly, the asymmetric higher-order rational solitons on the left and right sides are mirror-symmetrical to each other, which coincides with the symmetry of the modulation instability distribution. These results can deepen our understanding of the relationship between nonlinear excitation and modulation instability and enrich our knowledge about higher-order nonlinear excitations.
我们研究了三阶和四阶效应共存的非线性光纤中非线性局域波结构与调制稳定性区域分布特征之间的关系。在背景频率和背景幅度平面上，调制稳定性区域由左、右两侧的两条对称曲线和对称轴上的一个点组成。我们发现，在调制稳定性区域的不同位置，高阶激发特性明显不同。它们的激发特性与系统的调制不稳定性分布特征密切相关。结果表明，在左、右稳定曲线处激发不对称高阶有理孤子，而在稳定点处激发对称高阶有理孤子。有趣的是，左、右两侧的不对称高阶有理孤子是彼此镜像对称的，这与调制不稳定性分布的对称性一致。这些结果可以加深我们对非线性激发与调制不稳定性之间关系的理解，丰富我们对高阶非线性激发的认识。
