Review of heavy-nucleus-acoustic nonlinear structures in cold degenerate plasmas

Ultra-dense degenerate quantum plasma is an omnipresent ingredient in astrophysical compact objects (viz., neutron stars, white dwarfs, black holes, etc.) as well as in the plasma produced laboratory devices (viz., quantum diodes, quantum dots, quantum free electron lasers, thin metal film, etc.). These ultradense plasmas in astrophysical environments are assumed to be composed of non-relativistically non-degenerate heavy nuclei (viz., $$_{26}^{56}Fe$$ or $$_{37}^{85}Rd$$ or $$_{42}^{96}Mo$$ , etc.), non-relativistically degenerate light nuclei (viz. $$_1^1H$$ or $$_2^4He$$ or $$_6^{12}C$$ or $$_8^{16}O$$ , etc.), and relativistically degenerate electron gas. The nonlinear features of different collective modes (such as solitary waves, shock waves as well as envelope solitons and rogue waves) associated with the dynamics of the heavy-nucleus species in such extremely dense quantum plasmas are presented. The plasma fluid model, which describes the dynamics of heavy-nucleus-acoustic waves, is governed by set of hydrodynamical equations consisting of continuity and momentum equation for the heavy-nucleus fluid along with the Poisson equation for the net charge densities of inertialess degenerate electron and light nucleus species as well as inertial heavy-nucleus species. The degeneracy effects of the electron and light nucleus species, which arise due to Heisenberg’s uncertainty principle, on the nonlinear characteristics of small as well as arbitrary amplitude heavy nucleus-acoustic waves are rigorously analyzed by employing different standard mathematical methods. The influence of different key plasma parameters, especially the number densities of degenerate electron, light nucleus, and heavy-nucleus species on the propagation properties of different nonlinear waves (viz., solitons, shocks, envelope modes, and rogue waves), is discussed. The results should be useful in better understanding the properties of different localized nonlinear structures in multi-component cold degenerate quantum plasmas which are exist in astrophysical compact objects (e.g., white dwarfs, neutron stars, etc.) and in high-density plasma experiments.