Multi-Sasa Satsuma rogue events and multi-wave trains generation in a nonlinear left-handed transmission line

We demonstrate at the first time that the left-handed transmission line with varactor diodes can support higher-order effects. So, we establish at the first time, a nonlinear Schrödinger equation including second-, third- and fourth- order dispersions and self- and quintic-phase modulations. We use collective coordinate’s theory in order to give a good characterization of the light pulse. Moreover, we introduce a new Ansatz function called “type I Ansatz function” with seven coordinates compared to the conventional Ansatz function with six coordinates. The additional coordinate called “nonlinear phase” will give supplemental details on internal deformation which occurs during the propagation of the soliton light pulse. We find that the action of quintic-phase modulation on soliton light pulse leads to the generation of Peregrine solitons and several narrow wave trains. The introduction of third-order dispersion induces the appearance of multi-Sasa–Satsuma rogue events. Further, we introduce fourth-order dispersion and we assist to the generation of Parallel wave trains associated with strange wave’s field. Considering an increase in frequency combined to the action of all those effects, the precedent Parallel wave trains are changed into conventional Sasa–Satsuma rogue waves. Furthermore, we present physical conditions and theoretical frequencies leading to the generation of those specific extreme events. The new introduced Ansatz function improves the comprehension of rogue wave’s mechanism of generation.