二维时间分数阶Burgers-Fisher方程的李对称分析、精确解和守恒律  

Lie Symmetry Analysis,Exact Solution,and Conservation Law of Two-dimensional Time Fractional Burgers-Fisher Equation

作　　者：李连忠 姜欣欣 郭欣悦 LI Lian-zhong;JIANG Xin-xin;GUO Xin-yue(School of Science,Jiangnan University,Wuxi,Jiangsu 214122;Linyi Qihang Middle School,Linyi,Shandong 276000)

机构地区：[1]江南大学理学院,江苏无锡214122 [2]临沂启航中学,山东临沂276000

出　　处：《泰山学院学报》2024年第6期62-70,共9页Journal of Taishan University

摘　　要：一维经典Burgers-Fisher方程是流体动力学模型中一个重要方程,2017年由Macías-Díaz和González推广到二维情况。在两种方程演化过程的启发下,首先提出了一个扩展二维时间分数阶Burgers-Fisher方程并进行了李对称分析,得到了简化后的偏微分方程;其次利用幂级数展开方法得到了简化方程的收敛的精确解并绘制了图像;最后利用Ibragimov的新守恒定律,推导出了方程的非局部守恒定律。The one-dimensional classical Burgers-Fisher equation is an important equation in fluid dynamics models,which was extended to the two-dimensional case by Macías-Díaz and González in 2017.Inspired by the evolution process of two equations,an extended two-dimensional time fractional Burgers-Fisher equation was first proposed and subjected to Lie symmetry analysis,Firstly,an extended two-dimensional time fractional Burgers-Fisher equation was proposed and subjected to Lie symmetry analysis,resulting in a simplified partial differential equation;Secondly,the exact solution for the convergence of the simplified equation was obtained using the power series expansion method and a graph was plotted;Finally,using Ibragimov's new conservation law,the non local conservation law of the equation was derived.

关 键 词：时间分数阶Burgers-Fisher方程 分数阶李对称 幂级数解 守恒律 

分 类 号：O175.29[理学—数学]