Liu Chong, Yang Zhan-Ying, Yang Wen-Li
School of Physics, Northwest University, Xi'an 710069, China.
Chaos. 2018 Aug;28(8):083110. doi: 10.1063/1.5025632.
We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolute difference of group velocities of SR breathers coincides exactly with the linear MI growth rate. This link holds for a series of nonlinear Schrödinger equations with infinite-order terms. For the particular case of SR breathers with opposite group velocities, the growth rate of SR breathers is consistent with that of each quasi-Akhmediev breather along the propagation direction. Numerical simulations reveal the robustness of different SR breathers generated from various non-ideal single and multiple initial excitations. Our results provide insight into the MI nature described by SR breathers and could be helpful for controllable SR breather excitations in related nonlinear systems.
我们报告了扎哈罗夫 - 格拉什超正则（SR）呼吸子（由一对准艾哈迈德耶夫呼吸子形成）与有趣的不同非线性传播特性和调制不稳定性（MI）之间的确切联系。这表明SR呼吸子群速度的绝对差值恰好与线性MI增长率一致。这种联系适用于一系列带有无穷阶项的非线性薛定谔方程。对于具有相反群速度的SR呼吸子的特殊情况，SR呼吸子的增长率与每个准艾哈迈德耶夫呼吸子沿传播方向的增长率一致。数值模拟揭示了从各种非理想单初始激发和多初始激发产生的不同SR呼吸子的稳健性。我们的结果为SR呼吸子所描述的MI性质提供了见解，并且可能有助于在相关非线性系统中可控地激发SR呼吸子。
