尘埃等离子体中时间分数阶mZK模型及其精确解

Time Fractional Order mZK Model and Its Exact Solution in Dust Plasma

为了更加全面地了解尘埃等离子体中尘埃声孤波的传播特性与周期性,从(2+1)维低频冷尘埃等离子体的无量纲化方程出发,利用多尺度分析与约化摄动法推导(2+1)维mZK(modifed Zakharov-Kuznetsov)方程以描述尘埃声孤波的传播规律.与传统KdV模型相比,该模型的非线性更高,其可描述孤波在面上的传播.进一步基于分数变分法与半逆法,获得了(2+1)维时间分数阶mZK方程,最后运用(G′/G2)展开法求解出尘埃等离子体中(2+1)维mZK时间分数阶方程的系列新精确解.

In order to understand the propagation characteristics and periodicity of dust acoustic solitary wave in dust plasma more comprehensively,this paper deduces the(2+1)dimensional mZK(modifed Zakharov-Kuznetsov)equation by using multi-scale analysis and reduced perturbation method from the dimensionless equation of(2+1)dimensional cold dust plasma to describe the propagation law of dust acoustic solitary wave.Compared with the traditional KdV model,this model has higher nonlinearity and can describe the propagation of solitary wave on the surface.Based on the fractional variational method and the semi-inverse method,the(2+1)dimensional time fractional order mZK equation is obtained,and the new series of exact solutions of(2+1)dimensional time fractional order mZK equation in dust plasma are obtained by using the(G′/G2)expansion method.