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The nonlinear propagation of waves (specially solitary waves) in an ultra-relativistic degenerate dense plasma (containing ultra-relativistic degenerate electrons and positrons, cold, mobile, inertial ions, and negatively charged static dust) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg de-Vries equation have been derived whose numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The existence of solitary structures has been also verified by employing the pseudo-potential method. The implications of our results in astrophysical compact objects have been briefly discussed

Propagation of Electrostatic Waves in an Ultra-Relativistic Dense Dusty Electron-Positron-Ion Plasma