Mathematical modeling of chirped modulated waves along a multi-coupled nonlinear electrical transmission line with dispersive elements

Abstract

This work presents a mathematical modeling of chirped modulated waves propagating along a two-dimensional nonlinear electrical transmission line consisting of nonlinear dispersive and purely nonlinear capacitive elements. Combining the rotating-wave approximation technique with the perturbation method, we derive a two-dimensional extended nonlinear Schrödinger equation with self-steepening and self-frequency shift, that predicts the formation and propagation of a very rich variety of soliton-like waves including bright, dark, kink, and double-kink soliton-like waves with nonlinear chirp in a multi-coupled nonlinear electrical transmission network with dispersive elements. Using this model equation, parameter domains are delineated in which these modulated waves exist. The parameter domains are found to be strongly dependent on the dispersive elements of the network system. Through exact solutions of the amplitude equation, we investigate the dynamics of chirped modulated waves along the network system under consideration. Our results show that the nonlinear chirp associated with each of the found soliton-like pulses is directly proportional to the wave intensity and is saturated at some finite value as the propagation coordinate approaches its asymptotic value. Also, we show that increasing the number of the network lines decreases the propagating speed of the soliton-like pulses. Most importantly, theoretical analysis show that chirping of found network pulses can be controlled by varying the self-steepening term and self-frequency shift. The validity of analytical results and the robustness of these chirped soliton-like voltage signals which may have important applications in signal processing systems are confirmed by numerical simulations. The results of our study may be launched in long distance telecommunication lines involving higher-order nonlinearities of the fiber.