极光区等离子体时间分数阶KdV方程的变分方法
Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods
摘要：
本文用约化微扰法导出了小振幅静电波的Korteweg-de Vries（KdV）方程。时间分数阶KdV方程的拉格朗日量以与正则KdV方程的拉格朗日量类似的形式使用。这个拉格朗日函数的变化导致欧拉-拉格朗日方程，导致时间分数KdV方程。利用分数阶导数的Riemann-Liouvulle定义描述分数阶KdV方程中的时间分数阶算子。用He给出的变分迭代法求解了时间分数阶KdV方程。对初始条件为A0*sech（cx）^2的解进行了计算。数值研究已经取得了使用等离子体参数接近这些值对应的昼侧极光区。讨论了时间分数参数对静电孤立子结构的影响。
英文摘要：
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone. The effects of the time fractional parameter on the electrostatic solitary structures are presented.
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