Ion acoustic solitary and shock waves in strongly coupled degenerate plasma with relativistic effects

Abstract

Abstract The ion acoustic solitary and shock waves are studied in strongly coupled nonrelativistic and relativistic plasma. The wave profile has been discussed for the kinetic and hydrodynamic regimes. The ions are considered to be strongly coupled, and electrons as degenerated and relativistic to deal with nonlinear waves using continuity and Poisson’s equations together with generalized hydrodynamical (GH) and quantum hydrodynamical (QH) models. The reductive perturbation method is used to formulate Korteweg–de Vries (KdV) and Korteweg–de Vries Burgers (KdVB) equations in both nondegenerate and degenerated cases. The effects of relativistic, degeneracy parameter and longitudinal viscosity coefficient on the profile of nonlinear waves are discussed. The amplitude and width of a shock in both nonrelativistic and ultrarelativistic cases increase with an increase in the viscosity coefficient, while with an increase in the electron diffraction parameter, the amplitude and width of the shock wave increase, and for a solitary wave decreases in both the nonrelativistic and ultra-relativistic cases. It is also shown that solitary ion acoustic wave propagates with more energy in nonrelativistic plasma than ultrarelativistic. The results of the work will be useful, for example, for astrophysics to understand the process of wave propagation in dense astrophysical bodies.