一类广义KdV方方程的留数对称和CRE可解解性  

Residual symmetry and consistent Riccati expansion solvability for a class of GKdV equations

作　　者：吕梓帆 张顺利 LüZifan;Zhang Shunli(School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2022年第2期191-199,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11775047)。

摘　　要：基于Painleve′截断展开方法得到一类广义KdV方程的非局域留数对称和Backlund变换,并利用Lie定理将其局域化,进而对方程进行约化求解.然后,利用CRE可解性方法得到方程新的相互作用解,并作出解的波形图.In this paper, the nonlocal residual symmetry and Backlund transformation of a class of GKdV equations are obtained based on Painlev′e truncation expansion method, and the symmetry is localized by using Lie theorem. Then, the new interaction solution of the equation is obtained by using consistent Riccati expansion solvability, and the waveform of the solution is given by Maple software.

关 键 词：广义KDV方程 留数对称 相互作用解 CRE可解性 

分 类 号：O175.2[理学—数学]