Ginzburg-Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line

Abstract

This work is devoted to investigation of nonlinear transmission line containing nonlinear capacitors. In the work we study the stability of a set of 2 coupled Ginzburg-Landau (GL) equations derived from a model of nonlinear transmission line. After deriving the main differential equation for the voltage, we consider an expansion of the voltage amplitudes for 2 travelling waves and obtain the time and space Ginzburg-Landau differential equations for these amplitudes. We next study the existence and stability of the modulated amplitude waves in the complex plane, and show the existence of solition-like solutions.