  A theoretical investigation has been made to study the cylindrical and
spherical electron-acoustic shock waves (EASWs) in an unmagnetized,
collisionless degenerate quantum plasma system containing two distinct groups
of electrons (one inertial non-relativistic cold electrons and other
inertialess ultra-relativistic hot electrons) and positively charged static
ions. By employing well known reductive perturbation method the modified
Burgers (mB) equation has been derived. It is seen that only rarefactive shock
waves can propagate in such a quantum plasma system. The effects of degenerate
plasma pressure and number density of hot and cold electron fluids, nonplanar
geometry, and positively charged static ions are responsible to modify the
fundamental properties of EASWs. It is also observed that the properties of
planar mB shocks are quite different from those of nonplanar mB shocks. The
findings of the present investigation should be useful in understanding the
nonlinear phenomena associated with nonplanar EAWs in both space and laboratory
plasmas.
