  A theoretical investigation has been carried out to examine the ion-acoustic
shock waves (IASHWs) in a magnetized degenerate quantum plasma system
containing inertialess ultra-relativistically degenerate electrons, and
inertial non-relativistic positively charged heavy and light ions. The Burgers'
equation is derived by employing reductive perturbation method. It can be seen
that under consideration of non-relativistic positively charged heavy and light
ions, the plasma model supports only positive electrostatic shock structure. It
is also observed that the charge state and number density of the
non-relativistic heavy and light ions enhance the amplitude of IASHWs, and the
steepness of the shock profile is decreased with ion kinematic viscosity
($\eta$). The findings of our present investigation will be helpful in
understanding the nonlinear propagation of IASHWs in white dwarfs and neutron
stars.
