EFFECT OF NONLINEAR COUPLING ON MODULATIONAL INSTABILITY IN NONLINEAR TRANSMISSION LINES

We study the effect of nonlinear coupling on nonlinear electrical transmission lines (NETLs). By using the semi-discrete approximation, we derive the uncoupled nonlinear Schrödinger equations describing the propagation through the network. Analytical and numerical studies present a good agreement. We show that by coupling NETLs in this way, the propagation of waves in each line can be alternatively described by two nonlinear Shrödinger equations according to the direction of the current flow through the coupling branch. It also comes from this study that the nonlinear coupling adds the domains of modulational instability (MI) of each line. We show that a small variation of the nonlinear elements used in the coupling branch can change significantly the behavior of the network. Results which are found in this study can be applied in the context of molecular or atomic chains and in telecommunication systems for example.