The degenerate relativistic quantum plasma (DRQP) systems are not only common in space (viz., white dwarfs, neutron stars, and black holes), but also common in laboratory devices (viz., solid density plasmas, ultra-cold plasmas formed from laser-cooled atoms by the ionizing action of an intense laser pulse, and laser produced plasmas formed from solid targets irradiating by intense laser). The nonlinear wave phenomena in such a multi-component DRQP medium has opened up a new big window of research and also got a lot of interest to the plasma physicists. The main aim of this work is to examine the basic features of electrostatic solitary structures (in the form of envelope soliton and pulse soliton), shock waves, and rogue waves, in a multi-component DRQP medium, theoretically, and numerically. A multi-scale perturbation approach will be adopted to model/analyze the envelope type solitary modes via the cubic nonlinear Schrodinger equation (NLSE), while the reductive perturbation technique will be employed to model the pulse type solitary excitations and shock waves via the KdV/mKdV equation and Burgers'/KdVB equation, respectively. Finally, considering the nonplanar geometry the cKdV equation will be derived to analyse the cylindrical nature of electrostatic solitary waves in DRQP system. This study should be useful in understanding the basic features of the nonlinear waves in a multi-component degenerate quantum plasmas, in connection with astrophysical compact objects (e.g., white dwarfs, neutron stars, etc.)
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