非线性时间分数阶色散方程的分支问题与精确解研究  

Studies on bifurcations and exact solutions of nonlinear time fractional dispersive equations

作　　者：张慧 芮伟国 ZHANG Hui;RUI Wei-guo(School of General Education,Mianyang City College,Mianyang 621000,China;School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]绵阳城市学院通识教育学院,四川绵阳621000 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《东北师大学报（自然科学版）》2022年第2期27-35,共9页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11361023);重庆市科委项目(cstc2018jcyjAX0766)。

摘　　要：研究了非线性时间分数阶色散方程精确解的存在性问题及动力学性质.通过分析在不同参数条件下由时间分数阶色散方程导出的系统相图,获得了光滑周期解、有界解、具有compacton性质的稳定解.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.The method of combining the separation variable method and the dynamic system method is used to study the existence and dynamic properties of the exact solution of the nonlinear time fractional dispersive equation.By analyzing the phase diagram of the system derived from the time fractional dispersion equation under different parameters, the smooth periodic solutions, bounded solutions and stable solutions with compacton properties are obtained.The dynamic evolution behavior of some exact solutions is shown intuitively by means of image simulation.

关 键 词：时间分数阶色散方程 动力系统方法 分离变量法 相图分支 精确解 

分 类 号：O193[理学—数学]