非广延等离子体中非线性离子声波的数值研究:分数阶模型  

Numerical Investigation on Nonlinear Ion-acoustic Waves in a Nonextensive Plasma:Fractional Model

作　　者：赵梅妹[1] ZHAO Mei-mei(School of Engineering and Technology,Xi'an Fanyi University,Xi'an 710105)

机构地区：[1]西安翻译学院工程技术学院,西安710105

出　　处：《工程数学学报》2020年第4期511-520,共10页Chinese Journal of Engineering Mathematics

基　　金：陕西省科技厅自然科学基金(2020JQ-008);西安翻译学院科研项目(20A05).

摘　　要：本文的主要目的是研究非磁化等离子体中离子声波的非局部非线性行为,该非磁化等离子体是由正离子、满足非广延分布的电子、以及带有负电荷的静止的尘埃颗粒构成的.在流体力学基本方程组中,本文引入修正的Riemann-Liouville分数阶导数并建立了分数阶模型,结合约化摄动法推导出描述离子声波运动的Korteweg de Vries (Kdv)方程.本文采用Chebyshev-Legendre-Galerkin (CLG)拟谱方法数值求解该方程,并分析等离子体参数对离子孤立声波结构的影响.本文的研究结果表明:提高分数阶导数的阶数能够提升孤立波的振幅.该结果将有助于更好地理解天体物理和实验室等离子体中的非线性波动现象.The paper is intended to study the nonlinear behavior of planar ion-acoustic waves in an unmagnetized plasma consisting of positive ions,non-extensive electrons,positrons,and stationary negatively charged dust grains.In the basic fluid equations,Jumarie’s modified Riemann-Liouville fractional derivative is adopted as the time derivative for the first time.Combined with the reductive perturbation method,a Korteweg-de Vries(KdV)equation is derived for the motions of ionacoustic waves.The Chebyshev-Legendre-Galerkin(CLG)pseudospectral method is applied to solve this KdV equation numerically for analyzing how the plasma parameters influence the soliton structures of ion-acoustic waves.It concludes that increasing the order of fractional derivatives can increase the amplitude of solitary waves,which enables a better understanding of nonlinear wave phenomena in both astrophysical environments and laboratory plasma experiments.

关 键 词：分数阶微积分 KDV方程 谱方法 离子声波 

分 类 号：O241.82[理学—计算数学]