Kengne Emmanuel, Liu WuMing
School of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua 321004, China.
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. 2020 Jul;102(1-1):012203. doi: 10.1103/PhysRevE.102.012203.
A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using the cubic-quintic nonlinear Schrödinger (CQ-NLS) equation with a cubic nonlinear derivative term. The results show that, in the semidiscrete limit, the voltage for the transmission network is described in some cases by the CQ-NLS equation with a derivative term that is derived employing the reductive perturbation technique. A one-parameter first-order rational solution of the derived CQ-NLS equation is presented and used to investigate analytically the dependency of the characteristics of the first-order rouge wave parameters on the electric transmission network under consideration. Our results show that when we change the quintic nonlinear and nonlinear dispersion parameter, the first-order nonautonomous rogue wave transforms into the bright-like soliton. Our results also reveal that the shape of the first-order nonautonomous rogue waves does not change when we tune the quintic nonlinear and nonlinear dispersion parameter, while the quintic nonlinear term and nonlinear dispersion effect affect the velocity of first-rogue waves and the evolution of their phase. We also show that the network parameters as well as the frequency of the carrier voltage signal can be used to manage the motion of the first-order nonautonomous rogue waves in the electrical network under consideration. Our results may help to control and manage rogue waves experimentally in electric networks.
本文对一维改进的诺戈奇非线性输电网络进行了理论研究，该网络具有由大量相同部分组成的色散元件。利用带有三次非线性导数项的三次-五次非线性薛定谔（CQ-NLS）方程，对该网络中具有五次非线性和非线性色散效应的一阶非自治 rogue 波进行了预测和分析。结果表明，在半离散极限情况下，输电网络的电压在某些情况下由采用约化摄动技术导出的带有导数项的 CQ-NLS 方程描述。给出了导出的 CQ-NLS 方程的单参数一阶有理解，并用于分析研究一阶 rouge 波参数特性对所考虑的输电网络的依赖性。我们的结果表明，当改变五次非线性和非线性色散参数时，一阶非自治 rogue 波转变为类亮孤子。我们的结果还表明，当调整五次非线性和非线性色散参数时，一阶非自治 rogue 波的形状不变，而五次非线性项和非线性色散效应影响一阶 rogue 波的速度及其相位演化。我们还表明，网络参数以及载波电压信号的频率可用于控制所考虑的电网中一阶非自治 rogue 波的运动。我们的结果可能有助于在电网中通过实验控制和管理 rogue 波。
