Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Abstract

Herein, the behavior of the soliton light pulse when quintic –nonlinearity, third‐order dispersion, and self‐steepening come into play in a nonlinear metamaterial for both negative index and absorption regimes is presented. The collective coordinate technique is used with the conventional Gaussian ansatz function to give a good characterization of the pulse profile. In addition to that the ansatz function presents six coordinates describing the internal behavior of the pulse during the propagation. Furthermore, the main goal of this work is to give an exact measure of the internal behavior leading to the generation of rogue events by collective coordinates. Some interesting results are found when the aforementioned linear and nonlinear effects gradually come into play. Among them is the generation of different forms of breather solutions, divergent wave trains, different forms of Sasa–Satsuma rogue waves, parabolic wave trains, Peregrine rogue waves, and “tree structures”. Some special phenomena known as deletion, translation, attenuation, and wall of waves are also shown. However, some new exact rogue solutions of the cubic–quintic nonlinear Schrödinger equation are also found.

Triangular Rogue Waves and Multi- Wave Trains Generation in a Chameleon Electrical Transmission Line

“…But, a rigorous observation shows that a significant increase of this parameter in left -handed propagation can amplify the radiations in the system in order to build up the wave's field depicted in Figure 6(c). This strange behavior is similar to that observed in metamaterials when absorption regime is considered [46,90,91,92,93]. Absorption regime is a particular case of left -handed regime (negative index regime).…”