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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

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.