Modulational instability of bright envelope soliton and rogue waves in ultra-relativistic degenerate dense electron-ion-positron plasma

Modulational instability and bright envelope solitons 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 Schrodinger equation has been derived and the growth rate of modulationally unstable ion acoustic wave in such plasma is 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 but there is no instability of the wave for any value of plasma parameters in such plasma. The solutions of ion acoustic envelope- solitons and rogue waves are obtained from the Nonlinear Schrodinger equation. The theoretical results have been analyzed numerically for different values of plasma parameters and the results are presented graphically. It is found that only bright envelope soliton would be excited in the ultra-relativistic 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.