Kengne E, Liu W M
Laboratory of Advanced Microsystems Engineering, Department of Computer Science and Engineering, University of Quebec at Outaouais, 101 St.-Jean-Bosco, Succursale Hull, Gatineau (PQ), Canada J8Y 3G5.
Laboratory of Condensed Matter Theory and Materials Computation, Institute of Physics, Chinese Academy of Sciences, No. 8 South-Three Street, ZhongGuanCun, Beijing 100190, China.
Phys Rev E. 2019 Jun;99(6-1):062222. doi: 10.1103/PhysRevE.99.062222.
A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such a NLS equation, the propagation of the first- and second-order rogue waves in the system is predicted and analyzed quantitatively and qualitatively. The rogue waves are expected to propagate for the bandwidth frequencies where the network may exhibit modulational instability. The effects of relevant network parameters on the characteristics of the rogue wave parameters are investigated. We show how to manipulate the relevant network parameters as well as the propagating frequency either to amplify the propagation of the rogue waves through the network, or to prevent rogue waves from being amplified in the network under consideration.
考虑一个由大量相同单元组成的具有色散元件的分布式输电网络。在半离散极限下使用约化摄动方法，我们表明该网络的电压由具有外部线性势的非线性薛定谔（NLS）方程描述。利用这样的NLS方程，对系统中一阶和二阶 rogue 波的传播进行了定量和定性的预测与分析。预计 rogue 波会在网络可能表现出调制不稳定性的带宽频率上传播。研究了相关网络参数对 rogue 波参数特性的影响。我们展示了如何操纵相关网络参数以及传播频率，要么放大 rogue 波在网络中的传播，要么防止在所考虑的网络中 rogue 波被放大。
