Nonlinear nucleus-acoustic waves in strongly coupled degenerate quantum plasmas

We report the evolutionary dynamics of nonlinear nucleus-acoustic wave patterns excitable in a strongly coupled self-gravitating complex quantum degenerate plasma (QDP) systems. It is inertially composed of strongly correlated non-degenerate heavy nuclei and weakly coupled degenerate light nuclei treated classically. It is thermally constituted of non-relativistic and ultra-relativistic degenerate lighter electrons behaving quantum mechanically. Application of nonlinear perturbation analysis results in a conjugated pair of extended Korteweg-de Vries (e-KdV) equations of unique mathematical shape. The constructed numerical tapestry shows the collective excitations of a new conjugational pair of nonlinear eigenmode structures of gravito-electrosatic origin. The electrostatic potential fluctuations evolve as a distinct family of stable periodic symmetric waves resembling regular soliton-antisoliton pulse-trains; in contrast, the gravitational counterparts evolve as a unique extended class of asymmetric oscillatory solitons and non-monotonous compressive dispersive asymmetric pulse-trains. The microphysical influential dependencies of the eigenstructural patterns on various sensible plasma multi-parametric factors are illustratively analyzed in both the non-relativistic (NR) and ultra-relativistic (UR) limits of the non-local quantum electronic dynamics. The applicability of the explored results in wave kinetic phenomenological processes naturalistically relevant in diversified compact astro-objects and their ambient hydrodynamic atmospheres is summarily outlined