Numerical simulations and bifurcation analysis of monotonic and oscillatory magnetosonic shock waves in a spin 1/2 degenerate quantum plasma

Nonlinear propagation of monotonic and oscillatory magnetosonic shock waves in a       magnetized degenerate quantum plasma consisting of ions and spin 1/2 nonrelativistic degenerate electrons is examined. The well-known reductive perturbation analysis is applied to obtain a Korteweg–de Vries–Burgers equation (KdVBE). The dissipative system of coupled nonlinear, ordinary, differential equations and the equilibrium points are hereby discussed on the basis of the bifurcation analysis. The nonlinear behaviour of shock wave structures is numerically investigated under the fourth order Runge-Kutta method. Numerical simulations show that the behaviour of monotonic and oscillatory magnetosonic shock waves depends essentially on the effects of quantum statistics and the spin magnetization energy. The present results may be helpful for an in-depth understanding of the nonlinear propagation of magnetosonic waves in magnetized degenerate quantum plasma, which occur in the dense astrophysical objects.