分数阶Fornberg-Whitham型方程的解析解及其演化现象  

Analytical solution and evolution of the fractional Fornberg-Whitham-type equations

作　　者：张慧 ZHANG Hui(School of General Education,City College,Southwest University of Science and Technology,Mianyang 621000,China)

机构地区：[1]西南科技大学城市学院,四川绵阳621000

出　　处：《云南民族大学学报（自然科学版）》2020年第5期458-463,共6页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11361023,61623020,11601048);重庆市科委项目(cstc2018jcyjAX0766)。

摘　　要：在变量分离法与齐次平衡原理相结合的方法的基础上,对解的假设结构稍加改进,利用改进后的方法分别研究时间分数阶、空间分数阶以及时间-空间分数阶三类非线性偏微分Fornberg-Whitham方程的精确解,并且对获得的精确解进行有关有界性、周期性和解随时间、空间发展的衰减性等方面的分析.通过图像模拟,展示了部分精确解的3维坐标图.In this paper,based on the combination of the variable separation method and the homogeneous balance principle,the hypothetical structure of the solution is slightly improved.By using the improved method,the exact solutions of three kinds of nonlinear partial differential Fornberg-Whitham time-fractional,space-fractional and time-space fractional equations are studied respectively.And the exact solutions obtained are analyzed in terms of boundedness,periodicity and decaying with time and space.Through image simulation,the three-dimensional coordinate map of partial accurate solution is shown.

关 键 词：齐次平衡法 变量分离法 精确解 分数阶Fornberg-Whitham 函数 

分 类 号：O175.29[理学—数学]