The three-dimensional instability of isothermal ion-acoustic (IIA) solitary waves is examined in a magnetized ultra-relativistic degenerate multicomponent plasma, comprising nondegenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons as well as positrons, by applying a small-k (long wavelength) expansion method. The nonlinear dynamics of IIA solitary waves in such a plasma model are governed by the nonlinear Zakharov–Kuznetsov equation. To perform the analysis, the instability criterion and the growth rate of the instability of IIA solitary waves have been obtained. A careful investigation shows that the amplitude, the width, the growth rate, and the instability of IIA solitary waves increase with the increasing chemical potential of electrons. The stable region of IIA solitary waves increases with the increasing fermion population and the angle between the directions of propagation and the uniform magnetic field. The present study may be helpful for elucidating the physical nature of nonlinear waves in compact objects such as white dwarfs and neutron stars where the concentration of degenerate ultra-relativistic electrons and positrons and their chemical potentials play a crucial role.

中文翻译：

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化学势对磁化超相对论简并多组分等离子体中等温离子声孤立波及其三维不稳定性的影响

在磁化超相对论简并多组分等离子体中检查等温离子声 (IIA) 孤立波的三维不稳定性，该等离子体包括非简并惯性热离子和超相对论简并无惯性电子以及正电子，通过应用小 k （长波长）扩展方法。这种等离子体模型中 IIA 孤立波的非线性动力学由非线性 Zakharov-Kuznetsov 方程控制。为了进行分析，已经获得了 IIA 孤立波的不稳定性判据和不稳定性的增长率。仔细研究表明，IIA孤波的振幅、宽度、增长率和不稳定性随着电子化学势的增加而增加。IIA孤立波的稳定区随着费米子数量的增加以及传播方向与均匀磁场之间的夹角而增加。本研究可能有助于阐明致密天体（如白矮星和中子星）中非线性波的物理性质，在这些天体中，简并超相对论电子和正电子的浓度及其化学势起着至关重要的作用。