时间分数阶Klein-Gordon型方程的精确解及其动力学性质

Exact Solutions of Time Fractional Klein-Gordon-Type Equations and Their Dynamical Properties

利用变量分离法与齐次平衡原理相结合的方法,对非线性时间分数阶Klein-Gordon型方程进行了研究,获得了这个非线性时间分数阶偏微分方程的各类精确解,进一步讨论了这些解的动力学性质,并且通过图像模拟的方式直观地展示了部分精确解的动力学演化行为和动力学现象.

In this work, based on the method of separation of variables combined with the homogeneous balance principle, we study the time-fractional Klein-Gordon-type equation. Different kinds of the exact solutions of this nonlinear time-fractional partial differential equation are obtained. Further, the dynamic properties of these solutions are discussed and, by means of the simulation way, the dynamic evolution behaviors and dynamic phenomena of some exact solutions are shown intuitively.