Nonlinear dynamics in strongly coupled quantum plasma

The properties of cylindrical and spherical modified ion-acoustic waves in a strongly coupled plasma (containing strongly correlated non-relativistic ions, weakly correlated relativistic (both non-relativistic and ultra-relativistic) electron and positron fluids, and positively charged static heavy ions) are investigated theoretically. The restoring force is provided by the degenerate pressure of the electron and positron fluids, whereas the inertia is provided by the mass of ions. The positively charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. By using reductive perturbation method, we have derived modified Burgers and Korteweg–de Vries equations. Their shock and solitary wave solutions are also numerically analyzed to understand the localized electrostatic disturbances. The basic features of modified ion-acoustic shock and solitary waves are found to be significantly modified by the effects of degenerate pressure of electrons, positrons, and ion fluids, their number densities, and various charge states of heavy ions. It is also observed that the amplitude of these shock and solitary profiles are maximum for spherical geometry, intermediate for cylindrical geometry, and minimum for planar geometry. The present analysis can be helpful for understanding different degenerate and relativistic phenomena in dense astrophysical environments as well as laboratory plasma systems.