title: Modulated waves and pattern formation in coupled discrete nonlinear LC transmission lines.
abstract: 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.
authors.affiliation: Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon. ndzanafabienii@yahoo.com
authors.forename: Fabien Ii
authors.initials: FI
authors.lastname: Ndzana
authors.forename: Alidou
authors.initials: A
authors.lastname: Mohamadou
authors.forename: Timoléon C
authors.initials: TC
authors.lastname: Kofané
authors.forename: Lars Q
authors.initials: LQ
authors.lastname: English