Nonlinear excitation and bi-directional propagation of heavy-nucleus-acoustic waves in multi-component unmagnetized quantum plasmas

The nonlinear dynamics and finitely small amplitude wave excitation of heavy-nucleus-acoustic waves (HNAWs) in extremely dense unmagnetized degenerate quantum plasma comprising inertial non-relativistically degenerate heavy-nuclei, non-inertial non-relativistically degenerate light-nuclei and ultra-relativistically degenerate electrons and positrons are theoretically investigated through the lens of the generalized Boussinesq equation. By employing Hirota’s method and Hereman’s technique, diverse $N$-soliton solutions are unveiled and revealing intriguing potential structures. Compressive profiles are observed in both subsonic and supersonic regimes, while rarefactive profiles are exclusively present only in the supersonic regime. Beyond traditional solitary waves, the present study identifies multi-solitons (one-, two-, three-) and Kuznetsov-Ma breathers (single, double) phenomena, showcasing their interactions with solitons and other breathers via higher-order solutions. Furthermore, it emphasizes the phase shift for two-soliton and three-soliton, the influence of plasma parameters on HNAWs and the key significance of wave number. This exploration highlights the rich nonlinear wave phenomena inherent in relativistic astrophysical plasmas, offering a fresh perspective on their complex dynamics.