A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such a NLS equation, the propagation of the first- and second-order rogue waves in the system is predicted and analyzed quantitatively and qualitatively. The rogue waves are expected to propagate for the bandwidth frequencies where the network may exhibit modulational instability. The effects of relevant network parameters on the characteristics of the rogue wave parameters are investigated. We show how to manipulate the relevant network parameters as well as the propagating frequency either to amplify the propagation of the rogue waves through the network, or to prevent rogue waves from being amplified in the network under consideration.

A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using the cubic-quintic nonlinear Schrödinger (CQ-NLS) equation with a cubic nonlinear derivative term. The results show that, in the semidiscrete limit, the voltage for the transmission network is described in some cases by the CQ-NLS equation with a derivative term that is derived employing the reductive perturbation technique. A one-parameter first-order rational solution of the derived CQ-NLS equation is presented and used to investigate analytically the dependency of the characteristics of the first-order rouge wave parameters on the electric transmission network under consideration. Our results show that when we change the quintic nonlinear and nonlinear dispersion parameter, the first-order nonautonomous rogue wave transforms into the bright-like soliton. Our results also reveal that the shape of the first-order nonautonomous rogue waves does not change when we tune the quintic nonlinear and nonlinear dispersion parameter, while the quintic nonlinear term and nonlinear dispersion effect affect the velocity of first-rogue waves and the evolution of their phase. We also show that the network parameters as well as the frequency of the carrier voltage signal can be used to manage the motion of the first-order nonautonomous rogue waves in the electrical network under consideration. Our results may help to control and manage rogue waves experimentally in electric networks.