Physical Review E
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.
Ndzana, Fabien II, Alidou Mohamadou, Timoléon C. Kofané, and Lars Q. English. "Modulated Waves and Pattern Formation in Coupled Discrete Nonlinear LC Transmission Lines." Physical Review E 78, no.1 (2008): e016606. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.016606