Solitonic rogue waves dynamics in a nonlinear electrical transmission line with the next nearest neighbor couplings

Abstract

In this paper, a nonlinear transmission network with next-nearest-neighbor couplings is considered. We show how the propagation dynamics of the waves through the network can be described by a nonlinear Schrödinger (NLS) equation with an external linear potential after using the reductive perturbation method in the semidiscrete limit. Analytic solitonic solutions of the first and second order rogue waves in the system are predicted and analyzed. Taking into account the bandwidth frequencies where the network may exhibit modulational instability, the rogue waves propagation have been expected. One of the main results of our work is that with the introduction of the second neighbors parameter L3 in the network, two kind of rogue wave signals, either two bright rogue wave signals or one bright and one dark rogue wave signal, may simultaneously propagate at the same frequency through the network. The effects of both next-nearest-neighbor couplings parameter L3 and the strength χ of the linear potential on the dynamics of rogue waves through the network are also investigated. The characteristics of the rogue wave are investigated quantitatively and qualitatively with the introduction of the second neighbors couplings as relevant network parameters.