Impact of electron trapping in degenerate quantum plasma on the ion-acoustic breathers and super freak waves

The propagation of nonlinear ion-acoustic (IA) structures in a two-component plasma consisting of 'classical' ions and temperature degenerate trapped electrons is investigated. Using the reductive perturbation method, a nonlinear Schrödinger equation (NLSE) is obtained and the modulational instability (MI) of the ion acoustic waves (IAWs) is investigated. The regions of the stability and instability of the modulated structures are defined precisely depending on the MI criteria. The analytical solutions of the NLSE in the form of various types of freak waves, including the Peregrine soliton, the Akhmediev breather, and the Kuznetsov-Ma breather are examined. Moreover, the higher-order freak waves are presented. The characteristics of the rogue waves and their dependence on relevant parameters (the temperature of the degenerate trapped electrons and wavenumber) are investigated.