We consider the nonlinear ion acoustic wave induced by orbiting charged space debris objects in the plasma environment generated at the Low Earth Orbital (LEO) region. The generated nonlinear ion acoustic wave is shown to be governed by a forced Korteweg-de Vries (fKdV) equation with the forcing function dependent on the charged space debris function. For a specific relationship between the forcing debris function and the nonlinear ion acoustic wave, the forced KdV equation turns out to be a completely integrable system; where the debris function obeys a definite nonholonomic constraint. A special exact accelerated soliton solution (velocity of the soliton changes over time whereas its amplitude remains constant) has been derived for the ion acoustic wave for the first time. On the other hand, the amplitude of the solitonic debris function varies with time, and its shape changes during the propagation. Approximate ion acoustic solitary wave solutions with time varying amplitudes and velocities have been derived for different types of weakly localized charged debris functions. Possible applications of the obtained results in space plasma physics are stated along with future directions for research.

中文翻译：

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在低地球轨道 (LEO) 等离子体区存在带电空间碎片时非线性离子声波的动力学研究

我们考虑了在低地球轨道 (LEO) 区域产生的等离子体环境中由轨道带电空间碎片物体引起的非线性离子声波。生成的非线性离子声波显示受强制 Korteweg-de Vries (fKdV) 方程控制，其强制函数取决于带电空间碎片函数。对于强迫碎片函数与非线性离子声波之间的特定关系，强迫KdV方程是一个完全可积的系统；其中碎片函数服从一个明确的非完整约束。首次为离子声波推导出了一种特殊的精确加速孤子解（孤子的速度随时间变化，而其振幅保持恒定）。另一方面，孤子碎片函数的幅度随时间变化，其形状在传播过程中发生变化。对于不同类型的弱局部带电碎片函数，已经推导出具有时变幅度和速度的近似离子声孤立波解。阐述了所得结果在空间等离子体物理学中的可能应用以及未来的研究方向。