Nonlinear ion acoustic waves in the presence of electron trapping with Landau quantization and thermal excitations induced smearing effects of the Fermi step function are investigated using the two-fluid theory in the vicinity of white dwarfs. In spite of the fact that the Kortweg de Vries (KdV) equation is derived within the confines of small amplitude approximation used in the reductive perturbation theory (RPT), it is found to admit solutions that exhibit outstanding capability of wave enhancement and have applications in the nonlinear wave propagation. It is found that enhancing the quantizing magnetic field and the electron thermal effects modify the spatial scale of the formation of the novel nonlinear structures reported for our model. Interestingly, it is found that, unlike the solitary and periodic structures, the choice of space and time coordinates affects the structure of these solutions. Interaction of these solutions with a stable nonlinear structure are also studied.

中文翻译：

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致密磁等离子体中的非线性离子声波：使用朗斯基形式分析 KdV 方程的相互作用解，用于朗道抗磁性和热激发的电子捕获

使用白矮星附近的双流体理论研究了朗道量子化电子俘获和热激发引起的费米阶跃函数的涂抹效应的非线性离子声波。尽管 Kortweg de Vries (KdV) 方程是在还原微扰理论 (RPT) 中使用的小振幅近似的范围内导出的，但我们发现它所允许的解表现出出色的波增强能力，并且在非线性波传播。研究发现，增强量子化磁场和电子热效应可以改变我们模型报告的新型非线性结构形成的空间尺度。有趣的是，我们发现，与孤立结构和周期结构不同，空间和时间坐标的选择会影响这些解的结构。还研究了这些解与稳定非线性结构的相互作用。