Arbitrary amplitude solitary waves and double layers in an ultra-relativistic degenerate dense dusty plasma

Arbitrary amplitude solitary waves (SWs) and double layers (DLs) in an ultra-relativistic degenerate dense dusty plasma (containing ultra-relativistic degenerate ultra-cold electron fluid, inertial ultra-cold ion fluid, and negatively charged static dust) have been investigated by the pseudo-potential approach. It has been found that for δ=1δ=1 (where δ   is the ratio of nonlinear wave speed to linear wave phase speed) extremely large amplitude DLs with negative potential exist for μ=0.537μ=0.537 (where μ   is the ratio of dust charge density to ion charge density) and SWs with negative potential exist for 1>μ>0.5371>μ>0.537. It is also shown that for δ>1δ>1 only SWs with positive potential exist for 0⩾μ<0.5370⩾μ<0.537, but SWs with positive potential coexist with SWs or DLs with a negative potential for 0.537>μ>0.8510.537>μ>0.851. The implications of our results in some compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.