非线性时间分数阶Klein-Gordon方程的精确行波解  

Exact Traveling Wave Solutions for Nonlinear Time-Fractional Order Klein-Gordon Equation

作　　者：张练 刘小华 曾职云 ZHANG Lian;LIU Xiaohua;ZENG Zhiyun(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《西南师范大学学报（自然科学版）》2022年第3期36-43,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：贵州省科学技术厅项目([2019]1162)。

摘　　要：利用分数复变换将非线性时间分数阶Klein-Gordon方程转化为等价的非线性常微分方程;利用平面动力系统理论和方法给出了Klein-Gordon方程存在4个钟状孤波解、4个扭状孤波解和无穷多个周期解;通过辅助方程法给出了时间分数阶Klein-Gordon方程的4个扭状孤波解和周期解的精确表达式.By means of fractional complex transformation,the nonlinear time-fractional order Klein-Gordon equation has been transformed into an equivalent nonlinear ordinary differential equation.Four bell-shaped solitary wave solutions,four kink-shaped solitary wave solutions and infinite periodic wave solutions of the Klein-Gordon equation have been given in the theory and method of planer dynamical system.And the exact expressions of the four kink-shaped solitary and periodic wave solutions of the time fractional order Klein-Gordon equation been given in the auxiliary equation method.

关 键 词：平面动力系统理论 时间分数阶Klein-Gordon方程 辅助方程法 精确解 

分 类 号：O175.29[理学—数学]