Alternate backward and forward waves in a coupled nonlinear transmission line

Abstract

In this work, we investigate backward and forward waves in a coupled nonlinear discrete electrical lattice. It is made of several of the well-known Noguchi electrical transmission line that are transversely coupled to one another by an inductor $$L_{2}$$. Based on the linear dispersion law, we show that the behavior of this model depends on the wave frequency that it propagates. It can adopt purely right-handed, purely left-handed or composite right-/left-handed behaviors without changing its structure. It appears that for fixed line’s parameters, the network is right-handed for low frequencies and becomes left-handed for high frequencies. It also appears that the increase of the coupling linear inductor induces a decrease of the width of the bandpass filter in the left-handed region while it increases its width in the right-handed region. By means of a method based on the semi-discrete limit and in suitably scaled coordinates, we derive a two-dimensional NLS equation governing the propagation of slowly modulated waves in the network. The exact transverse bright solitary solution is found. Using this solution, we investigate numerically both right-handed and left-handed behaviours of the system and show how to manipulate the coupling inductor to modify the width and the motion of the bright solitary voltage signals in the network.