Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements. Issue 6 (30th April 2021) - Kengne, Emmanuel; Liu, WuMing
Abstract: A discrete nonlinear transmission network with dispersive element is considered. It is shown that the dynamics of slowly modulated waves propagating in this network are governed by a generalized cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift. Through the baseband modulational instability (MI) analysis, the conditions for this network to support the propagation of chirped super rogue waves (SRWs) are obtained. Based on the analytical rational solutions of the governed equation, chirped first‐ and second‐order super rogue waves are engineered in the nonlinear transmission network under consideration. The effects of the dispersive elements of the network on the chirped SRWs propagating in the network system are investigated. Particularly, it is shown that the introduction of the dispersive linear capacitance of the network enhances the baseband MI and both the derived SRWs and the corresponding frequency chirp are localized in both time and space. It is also shown that the structure of the frequency chirp depends strongly on the pulse self‐steepening and self‐frequency shift. Abstract : A discrete lossless nonlinear electrical transmission network with dispersive elements is considered. In the continuum limit, the theoretical analysis based on the cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift predicts possible propagation of rogue waves. Employing the phase engineering technique, the authors demonstrate that the competing cubic‐quintic nonlinearity induces propagating chirped super rogue waves in their network system.