Nonlinear Structures in Degenerate Astrophysical Compact Objects

The formation of electrostatic small but finite amplitude ion-acoustic (IA) shock waves and double layers (DLs) in a super-dense plasma composed of relativistic electron/positron fluid, non-degenerate viscous ion (positive/negative) fluid, and negatively charged static heavy ions has been theoretically investigated. The IA waves are the acoustic-type electrostatic waves where the restoring force is provided by the degenerate pressure of the electrons/ positrons, and the inertia is provided by the mass of positive/negative ions. The negatively charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The modified Burgers (mB) and Gardner (Gardner equation with additional dissipative term) equations have been derived by employing the reductive perturbation method, and analyzed in order to identify the basic features (polarity, width, phase speed, etc.) of the IA shock waves and DLs. It is pinpointed in this book that the basic features of these IA shock waves and DLs obtained from the analysis are significantly different from those obtained from the analysis of the standard Gardner or Burgers equation.