Peregrination, layers' and multi-peaks' generation induced by cubic-quintic-saturable nonlinearities and higher-order dispersive effects in a system of coupled nonlinear left-handed transmission lines

We establish a cubic-quintic-saturable nonlinear Schrodinger equation (CQSNLSE) with higher-order dispersive effects in a system of coupled nonlinear left-handed transmission lines. The coefficients of this equation are plotted to determine the most suitable frequencies range where those effects strongly act in the system. Furthermore, we apply collective coordinates' technique including a Gaussian Ansatz function with six coordinates to study in detail the wave propagation. Besides, some interesting results are found. (i) The system of coupled nonlinear left-handed transmission lines can support the propagation of the dark and bright solitons. (ii) Three phenomena emerge during the investigation. Among them, two have been induced by cubic-quintic-saturable nonlinearity known as fragmentation of the soliton light pulse and the layers' generation. The third phenomenon is the Peregrination due to the combined action of third-and fourth-order dispersions. (iii) The cubic-quintic-saturable nonlinearity acts on dark and bright solitons to induce one peak solutions, conventional, first-and second-forms of quadri-Sasa-Satsuma solutions, first-and second-forms of horizontal layered solitons, first-, second-and third-forms of distorted layered solitons, degraded Gaussian three peaks' solution, first-and second-forms of Gaussian, double, and triple Sasa-Satsuma solutions. (iv) The introduction of the combined action of third-and fourth-order dispersions leads to linear and complete chaotic Peregrine waves' fields, stairs-shaped multi-peaks' and triple Sasa-Satsuma solutions, degraded Gaussian double-Sasa-Satsuma solution, multi-peaks' solution associated with symmetric radiation lobes, and sawtooth layered soliton. It appears that all those exotic rogue events are strongly depended on the frequency and the coupling parameter.