Overtaking phenomenon of nonlinear ultra-low frequency multi-shock structures in ultra-relativistic degenerate plasmas

Overtaking collisions of nonlinear ultra-low frequency (NULF) shock waves are examined in a degenerate ultra-relativistic plasma, containing inertial mobile heavy-ion fluid and inertialess degenerate light ions and electrons. The well-known reductive perturbation analysis then is used to obtain a Burgers' equation (BE), which describes the propagation of ultra-low frequency shock waves in the plasma model. The Cole-Hopf transformation and the exponential function have been applied to get NULF multi-shock waves. Here, the findings illustrate that the excitation, amplitude, and steepness of overtaking collisions of NULF multi-shock waves and their electric fields are modified with the influence of heavy-ion kinematic viscosity. It is found that the amplitude and the steepness of NULF multi-shock waves increase with the decrease in the light-to-heavy ion density ratio. The numerical simulation gives rise to significant highlights on the dynamics of overtaking collisions of NULF multi-shock waves in astrophysical plasmas such as white dwarfs.