Modulational instability in a purely nonlinear coupled complex Ginzburg-Landau equations through a nonlinear discrete transmission line.
We study wave propagation in a nonlinear transmission line with dissipative elements. We show analytically that the telegraphers' equations of the electrical transmission line can be modeled by a pair of continuous coupled complex Ginzburg-Landau equations, coupled by purely nonlinear terms. Based on this system, we investigated both analytically and numerically the modulational instability (MI). We produce characteristics of the MI in the form of typical dependence of the instability growth rate on the wavenumbers and system parameters. Generic outcomes of the nonlinear development of the MI are investigated by dint of direct simulations of the underlying equations. We find that the initial modulated plane wave disintegrates into waves train. An apparently turbulent state takes place in the system during the propagation.
Ndzana
Fabien
F
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
D000465:Algorithms; D003198:Computer Simulation; D004559:Electric Wiring; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*