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The basic characteristics of cylindrical as well as spherical solitary and shock waves in degenerate electron-nucleus plasmas are theoretically investigated. The electron species is assumed to be cold, ultra-relativistically degenerate, negatively charged gas, whereas the nucleus species is considered a cold, non-degenerate, positively charged, viscous fluid. The reductive perturbation technique is utilized in order to reduce the basic equations (governing the degenerate electron-nucleus plasmas under consideration) to the modified Korteweg-de Vries and Burgers equations. The latter are numerically solved and analyzed to detect the basic characteristics of solitary and shock waves in such electron-nucleus plasmas. The nonlinear nucleus-acoustic waves are found to be propagated in the form of solitary as well as shock waves in such degenerate electron-nucleus plasmas. Their basic properties as well as their time evolution are significantly modified by the effects of cylindrical as well as spherical geometries. The results of this study is expected to be applicable not only to astrophysical compact objects, but also to ultra-cold dense plasmas produced in laboratory.

Cylindrical and Spherical Nucleus-Acoustic Solitary and Shock Waves in Degenerate Electron-Nucleus Plasmas