Multi-wave trains and Sasa - Satsuma freak events generation in an optical metamaterial

Abstract

In this work, we present a new Ansatz function called ”type I Ansatz function” with seven collective coordinates compared to the conventional Gaussian Ansatz function with six collective coordinates. We show that the additional coordinate called ”nonlinear phase” will allow us to improve the technique of measurement of internal excitation leading to the generation of rogue events. Moreover, the nonlinear phase coordinate will give supplemental details on the phase distortions during the generation of specific rogue events such as wall of waves, tree structures, double Kuznetsov - Ma breathers and Sasa - Satsuma rogue waves. The propagation will be modeled by a higher - order nonlinear Schrödinger equation when second - and third - order dispersions, self - and quintic - phase modulations and self - steepening come into play for negative index and absorption regimes. The conditions of stability of the soliton light pulse will also been investigated. The validity of our results is confirmed numerically by using a systematic computational approach.