广义Zakharov-Kuznetsov方程的动力学行为和解析解

研究了等离子体中用于描述低频静电离子-声波的广义Zakharov-Kuznetsov方程的动力学行为和解析解.分岔和相图分析结果表明,平衡点类型为鞍点和中心点,存在一系列周期轨线和同宿轨线,不同的非线性项、色散项系数会影响平衡点的类型和稳定性.此外,还得到了广义Zakharov-Kuznetsov方程的解析解,包括周期解、孤子解和冲击波解.

MAJin-Ying, MENGGao-Qing, YANZhan-Yuan

In this paper, dynamical behaviors and analytic solutions of the extended Zakharov-Kuznetsov equation, which can be used to describe the low-frequency electrostatic ion-acoustic waves in plasmas, have been investigated. The bifurcation analysis indicates that the equilibrium points are saddle and center points, and there exist a series of periodic and homoclinic orbits, while the types and stability of those equilibrium points are influenced by the coefficients of the nonlinear and dispersive terms. Moreover, the analytic solutions of the extended Zakharov-Kuznetsov equation have been constructed through the expanding function method, including the periodic, soliton and kink solutions.