Abstract
A Burgers' equation (BE) is obtained to examine the overtaking interactions of nonlinear ultra-low frequency (ULF) shock waves, in two cases, in non-relativistic and ultra-relativistic degenerate plasmas consisting of inertial mobile heavy-ion fluid and inertialess light ions and electrons. The Cole-Hopf transformation and the exponential function have been employed to obtain nonlinear ULF multi-shock structures. From the careful analysis, it is found that the overtaking collisions of ULF multi-shock waves and their electric fields are significantly modified with the influence of heavy-ion kinematic viscosity. It is shown that the amplitude and the steepness of ULF multi-shock waves increase with the decrease in the light-to-heavy ion density ratio. Numerical simulations of overtaking collisions are used to shed light on the dynamics of ULF multi-shock waves in astrophysical plasmas such as white dwarf stars.