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