(3+1)维时空分数阶mKdV-Zakharov-Kuznetsov方程的分支及解结构  

Bifurcations and Solution Structures of the(3+1)-dimensional Space-time Fractional mKdV-Zakharov-Kuznetsov Equation

作　　者：王美 孙峪怀 WANG Mei;SUN Yuhuai(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2023年第4期457-463,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12071323)。

摘　　要：通过动力系统分支理论构建(3+1)维时空分数阶mKdV-Zakharov-Kuznetsov方程的精确解.首先通过引入分数阶复变换将(3+1)维时空分数阶mKdV-Zakharov-Kuznetsov方程化为常微分方程组,然后借助Hamilton系统得到不同条件下的分支相图,最后根据分支相图给予不同演化轨道,构建演化方程的一系列精确解,这些精确解包含双曲函数解、Jacobi椭圆函数解和三角函数解.The exact solution of(3+1)-dimensional space-time fractional mKdV-Zakharov-Kuznetsov equation is constructed by means of the bifurcation theory of dynamical systems.Firstly,the(3+1)-dimensional space-time fractional mKdV-Zakharov-Kuznetsov equation is transformed into ordinary differential equations by introducing fractional complex transformation.Then,the branch phase diagrams under different conditions are obtained by using Hamilton system.Finally,a series of exact solutions of the evo-lution equation are constructed by giving different evolution paths according to the branch phase diagrams.These exact solutions include hyperbolic solutions,Jacobi elliptic function solutions and trigonometric function solutions.

关 键 词：mKdV-Zakharov-Kuznetsov方程 精确解 分数阶复变换 分支相图 

分 类 号：O175.13[理学—数学] O175.6[理学—基础数学]