FORMULATIONS AND ANALYSIS OF NONLINEAR MODIFIED BURGERS EQUATIONS IN A DENSE PLASMA SYSTEM WITH RELATIVISTIC ELECTRON FLUIDS

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.