The nonlinear propagation of self-gravitational shock structures (SGSSs) in a self-gravitating, super-dense, degenerate quantum plasma system (containing non-degenerate extremely heavy nuclei and ultra-relativistic degenerate electrons) has been investigated. The well-known reductive perturbation technique, which is valid in the small but finite amplitude limit, has been used to examine the nonlinear propagation of these SGSSs in such degenerate quantum plasma systems. The nonlinear dynamics of these SGSSs has been found to be governed by the Burgers equation, which is derived analytically and solved numerically in planar coordinates. These SGSSs in such plasma systems are shown to be formed due to the presence of a viscous force (which is the source of dissipation) acting on inertial extremely heavy nuclei species of the plasma system. The fundamental properties (viz., amplitude, width, speed, etc.) of these SGSSs are influenced in the ultra-relativistic limit. Our considered plasma model and the numerical analysis of the Burgers equation can be applied to astrophysical compact objects like neutron stars.

中文翻译：

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自引力、超密、简并量子等离子体中的自引力激波结构

已经研究了自引力、超密、简并量子等离子体系统（包含非简并极重核和超相对论简并电子）中自引力激波结构 (SGSS) 的非线性传播。众所周知的还原微扰技术在小但有限的幅度限制中有效，已被用于检查这些 SGSS 在此类简并量子等离子体系统中的非线性传播。已经发现这些 SGSS 的非线性动力学由 Burgers 方程控制，该方程是在平面坐标中解析导出和数值求解的。此类等离子体系统中的这些 SGSS 被证明是由于存在粘性力（这是耗散的来源）作用于等离子体系统的惯性极重核物质而形成的。这些 SGSS 的基本属性（即振幅、宽度、速度等）受到超相对论极限的影响。我们考虑的等离子体模型和 Burgers 方程的数值分析可以应用于像中子星这样的天体物理致密物体。