含非热电子的非线性电声波的孤波、爆炸波和有理解
Solitary, explosive and rational solutions for nonlinear electron-acoustic waves with non-thermal electrons
摘要：
对由冷电子流体、非热热电子和稳态离子组成的非磁化无碰撞等离子体中的电子声波传播进行了严格的理论研究。基于赝势方法，讨论了大振幅势结构和孤立波的存在性。本文用约化微扰法导出了小振幅静电波的Korteweg-de Vries（KdV）方程。本文提出了一种代数方法和计算机符号计算，大大超过了现有的双曲正切方法的适用范围，推广了双曲正切方法，得到了KdV方程的一系列精确解。数值研究已经使用接近对应于昼侧极光区的那些值的等离子体参数进行，揭示了不同的解决方案，即，钟形孤立脉冲、有理脉冲和在有限点处具有奇异性的解称为爆破解。本研究的结果可能适用于某些等离子体环境，如地球磁层。
英文摘要：
A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called blowup solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as terrestrial magnetosphere.
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