Modulational instability and associated multiple dark solitons in relativistically degenerate electron-positron-ion plasmas.

The modulational instability (MI) of the ion-acoustic waves (IAWs) is analyzed in an unmagnetized electron-positron-ion (EPI) plasma having relativistically degenerate electrons and positrons. For this purpose, the nonlinear Schrödinger (NLS) equation is derived using the derivative expansion method. The criteria for MI are numerically examined in the vicinity of pulsars, and it is observed that for both nonrelativistic and ultrarelativistic regimes, the EPI plasma remains modulationally stable. The nonlinear structures, derived using Hirota's method, are the dark envelope solitons. The dark solitons are further classified as black and gray solitons depending on the relation between the amplitude of the vacuum wave train and the propagation vector of the envelope soliton. The increase in the positron concentration is observed to stabilize the EPI system and is also found to reduce the amplitude of the dark envelope soliton. The interaction of black and gray, as well as the two gray solitons, shows that, being nonlinear waves, the condition of linear superposition is not met at the interaction point for dark envelope solitons. Furthermore, the spatial regime of the soliton interaction is reduced for the gray-gray envelope interaction compared to the black-gray envelope interaction, as well as the ultrarelativistic case compared to the nonrelativistic case. This study is novel as it discusses the interaction of dark solitons of the NLS in the context of plasmas for the first time. The results of the present model are beneficial to comprehend the dark envelope soliton interaction for astrophysical plasmas; however, by incorporating changes in the behavior of electrons and positrons, they are relevant for diverse conditions in laboratory and space plasmas.