时间分数阶KdV方程的精确解  

Exact solutions for the time-fractional KdV equations

作　　者：范万 芮伟国 洪晓春[2] FAN Wan;RUI Wei-Guo;HONG Xiao-Chun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650221,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]云南财经大学统计与数学学院,昆明650221

出　　处：《四川大学学报(自然科学版)》2025年第1期45-51,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11761075)。

摘　　要：与整数阶非线性偏微分方程相比,非线性分数阶偏微分方程的求解问题更加困难.本文利用半固定式变量分离法结合平面动力系统的相图法研究了时间分数阶KdV方程的精确解及其动力学行为.在特殊参数条件下,本文获得了方程的各类精确解,讨论了部分代表性解的性质,并绘制了解的图像,以便更好地理解方程的动力学行为.In comparison to the integer-order nonlinear PDEs,solving the nonlinear fractional PDEs is more difficult.In this paper,the exact solutions of the time-fractional KdV equation are considered by combining the separation method of semi-fixed variables and the phase diagram analysis of planar dynamical systems.Dynamical properties of the exact solutions are explored.Under particular parameter conditions,various exact solutions of the equation are obtained,dynamical properties of some representative solutions are discussed.To illuminate the dynamical behavior of the equation intuitively,three-dimensional figure of these solutions are given.

关 键 词：时间分数阶KdV方程 半固定式变量分离法 相图 精确解 

分 类 号：O175.2[理学—数学]