Shock waves in ultra-relativistic degenerate astrophysical e-p-i plasmas

In this work, we investigated the propagation of ion acoustic shock waves IAShWs in an ultra-relativistic degenerate plasma composed of positrons, electrons and ions in the presence of an external magnetic field. We have derived the KdV-B equation using the reductive perturbation technique and analyzed its solution graphically. The impact of the different plasma parameters (positron concentration, kinematic viscosity, strength of the magnetic field, obliqueness, relativistic effects, etc.) on the basic features of the IAShWs have been rigorously examined. It has been found that shock waves co-propagate with solitons in the ultra-relativistic case, whereas in the non-relativistic case, monotonic shock waves are in favor. Moreover, to highlight the relevance of our research in astrophysical environments, we have applied the plasma model to the surface of magnetic neutron stars where the plasma components are ultra-relativistic and degenerate. We have discerned that the parameters taken into account have significant effects on the nature and amplitude of the ion acoustic structures.