Ndzana Fabien Ii, Mohamadou Alidou, Kofané Timoléon C, English Lars Q
Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016606. doi: 10.1103/PhysRevE.78.016606. Epub 2008 Jul 29.
The conditions for the propagation of modulated waves on a system of two coupled discrete nonlinear LC transmission lines with negative nonlinear resistance are examined, each line of the network containing a finite number of cells. Our theoretical analysis shows that the telegrapher equations of the electrical transmission line can be reduced to a set of two coupled discrete complex Ginzburg-Landau equations. Using the standard linear stability analysis, we derive the expression for the growth rate of instability as a function of the wave numbers and system parameters, then obtain regions of modulational instability. Using numerical simulations, we examine the long-time dynamics of modulated waves in the line. This leads to the generation of nonlinear modulated waves which have the shape of a soliton for the fast and low modes. The effects of dissipative elements on the propagation are also shown. The analytical results are corroborated by numerical simulations.
研究了调制波在具有负非线性电阻的两条耦合离散非线性LC传输线系统上的传播条件，网络中的每条线路都包含有限数量的单元。我们的理论分析表明，输电线路的电报方程可以简化为一组两个耦合的离散复金兹堡-朗道方程。使用标准的线性稳定性分析，我们推导了作为波数和系统参数函数的不稳定性增长率表达式，然后得到调制不稳定性区域。通过数值模拟，我们研究了线路中调制波的长时间动力学。这导致了非线性调制波的产生，对于快模和慢模，其形状为孤子。还展示了耗散元件对传播的影响。数值模拟证实了分析结果。
