应用多项式完全判别系统方法求解时空分数阶复Ginzburg⁃Landau方程  

Solutions to Space⁃Time Fractional Complex Ginzburg⁃Landau Equations With the Complete Discrimination System for Polynomial Method

作　　者：胡艳 孙峪怀 HU Yan;SUN Yuhuai(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,P.R.China)

机构地区：[1]四川师范大学数学科学学院,成都610066

出　　处：《应用数学和力学》2021年第8期874-880,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12071323)。

摘　　要：研究了时空分数阶复Ginzburg⁃Landau方程.首先通过分数阶复变换将时空分数阶复Ginzburg⁃Landau方程转化为一个常微分方程.然后将常微分方程化为初等积分形式.最后用多项式完全判别系统法求得一系列精确解,其中包含有孤立波解、有理函数解、三角函数周期解、Jacobi椭圆函数双周期解.The space⁃time fractional complex Ginzburg⁃Landau equation was studied.Firstly,the space⁃time fractional complex Ginzburg⁃Landau equation was transformed into the ordinary differential equation through the fractional complex transform.Secondly,the ordinary differential equation was reduced to an elementary in⁃tegral form.Finally,a series of exact solutions including solitary wave solutions,rational function type solu⁃tions,triangle function type periodic solutions,and Jacobian elliptic function doubly⁃periodic solutions,were constructed with the complete discrimination system for polynomial method.

关 键 词：时空分数阶复Ginzburg⁃Landau方程 多项式完全判别系统方法 精确解 

分 类 号：O175[理学—数学]