Modulation Instability of Bright Envelope Soliton and Rogue Waves in Ultra-relativistic Degenerate Dense Electron–Ion–Positron Plasma

Abstract

Modulation instability, bright envelope soliton, and rogue waves of ion acoustic waves in dense plasma consisting of ultra-relativistic degenerate electrons and positrons, cold and mobile inertial ions, and negatively charged static dust particles have been investigated using Fried and Ichikawa method. Nonlinear Schrödinger equation has been derived and the growth rate of modulationally unstable ion acoustic wave in such plasma are discussed. It has been found that ion acoustic wave will be always modulationally unstable for all possible values of density of positrons, electrons, and charged dust particle. The solutions of envelope solitons and rogue waves are obtained from the nonlinear Schrödinger equation. The theoretical results have been analyzed numerically and graphically for different values of plasma parameters. It is found that only bright envelope soliton would be excited in the ultra-relativistic degenerate plasma. Our results are new and may be applicable for the study of nonlinear wave processes in relativistic degenerate dense plasmas of astrophysical objects, namely, in white dwarfs and neutron stars.