Rogue waves dynamics of cubic–quintic nonlinear Schrödinger equation with an external linear potential through a modified Noguchi electrical transmission network

Abstract

In this paper, we have considered a modified Noguchi nonlinear transmission network with a dispersive element. Using the reductive perturbation method in the semi-discrete limit, we show how wave dynamics in the network can be governed by a cubic–quintic nonlinear Schrödinger equation (CQ-NLSE) with an external linear potential. Through the modified Darboux transformation, we constructed the first, second and third order rogue wave solutions. Although the linear potential function Γ(τ) does not influence the instability criterion of waves propagating in the network, it has a significant effect on the dynamics of the amplitude, phase and shirp of rogue waves. Our results also reveal that it is possible both to predict the position where the amplitude of rogue waves reaches its maximum value and to reduce their spatial width.