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The formation of nucleus acoustic (NA) solitary waves (SWs) and shock structures (SSs) in a self-gravitating, degenerate, magnetized, quantum plasma system (containing non-relativistically heavy nuclei, non-relativistically light nuclei, and non-/ultra-relativistically degenerate electrons) has been theoretically investigated in both planar and non-planar geometries. The modfiied Korteweg-de Vries (mK-dV) and modified Burgers (mB) equations have been derived by employing the reductive perturbation method, and their solutions are obtained. The findings of our results obtained from these theoretical investigations may have important implications in understanding nonlinear phenomena in various space (viz. white dwarfs, non-rotating neutron stars, active galactic nuclei, cometary tails, etc.) and laboratory plasmas.