时间分数阶(2+1)-维扩展Fisher-Kolmogorov方程的精确解  

Exact Solutions of a Class of Time Fractional(2+1)-Dimensional Extended Fisher-Kolmogorov Equations

作　　者：王美乐 胡彦霞[1] WANG Meile;HU Yanxia(School of Mathematics and Physics,North China Electric PowerUniversity,Beijing 102206,China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《内蒙古大学学报（自然科学版）》2024年第3期232-243,共12页Journal of Inner Mongolia University：Natural Science Edition

基　　金：北京市自然科学基金资助项目(1232021)。

摘　　要：利用Lie方法对一类时间分数阶(2+1)-维扩展Fisher-Kolmogorov方程进行对称分析,并求得该方程的不变解,借助不变解对方程进行降维处理。对引入分数阶复变换得到的常微分方程运用辅助函数法,从而得到这类时间分数阶方程在参数满足各种不同情况下的精确解,包括三角函数解和孤波解等。最后绘出两类典型精确解的行波图。The Lie method is used to perform symmetric analysis of a class of time fractional(2+1)-dimensional extended Fisher-Kolmogorov equations for obtaining an invariant solution of the equations,and then the dimensionality reduction treatment is carried on the equations.The ordinary differential equations are obtained by introducing fractional order complex transformations.Based on the auxiliary function method,the exact solutions of the ODEs under various conditions which the parameters are satisfied are obtained,including trigonometric function solutions and solitary wave solutions.The relevant graphs of two typical exact solutions are drawn.

关 键 词：(2+1)-维扩展Fisher-Kolmogorov方程 Lie方法 辅助函数法 精确解 

分 类 号：O175[理学—数学]