Solitary waves and double layers in an ultra-relativistic degenerate dusty electron-positron-ion plasma

A rigorous theoretical investigation has been made on the formation of the nonlinear structures (viz., solitary waves, double layers) in a dusty electron-positron-ion plasma (containing inertialess degenerate electrons and positrons, cold, mobile, inertial ions, and negatively charged stationary dust). The pseudo potential method has been employed in this theoretical investigation. The basic features of the solitary waves and double layers, which are associated with positive ion dynamics and pressures of degenerate electrons and positrons, are identified. The co-existence of positive and negative solitary waves, and existence of either positive or negative double layers have been theoretically observed for certain range of different plasma parameters. The implications of our results in astrophysical compact objects have been briefly discussed.