Painleve变换法构造一类广义非线性偏微分方程的扭波解  

Kink Solutions for a Class of Generalized Nonlinear Partial Differential Equations Constructed by PainlevéTransformation Method

作　　者：卢霖 张超 郭力嘉 LU Lin;ZHANG Chao;GUO Lijia(School of Mathematics and Statistics,Hunan First Normal University,Changsha,Hunan 410205,China;Hunan Provincial Key Laboratory of Geotechnical Engineering for Stability Control and Health Monitoring,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China;School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]湖南第一师范学院数学与统计学院,湖南长沙410205 [2]湖南科技大学湖南省岩土工程稳定控制与健康监测重点实验室,湖南湘潭411201 [3]西南大学数学与统计学院,重庆400715

出　　处：《复旦学报（自然科学版）》2024年第6期695-702,共8页Journal of Fudan University：Natural Science

基　　金：湖南省自然科学基金青年项目(2017JJ3044);湖南省自然科学基金面上项目(2018JJ2073);湖南省教育厅科学研究重点项目(24A0667)。

摘　　要：关于广义的Benney方程和五阶KdV方程的精确解已有众多学者进行了研究,但大多侧重于寻找可积微分方程的亚纯解。本文基于Painleve变换法和多项式原理,直观地构造了不具有亚纯解结构的非线性不可积微分方程的精确解,并证明了该解是一种扭波解。进一步地,阐明了此方法可用于寻找其他更高阶的非线性不可积微分方程的扭波解。Many scholars have studied the exact solutions of the generalized Benney equation and the generalized fifth order KdV equation,but most of them focus on finding meromorphic solutions of integrable differential equations.In this paper,by using Painlevétransformation method and polynomial principle,exact solutions without meromorphic solution structure of the above nonlinear integrable PDEs are constructed,and it is proved that the solutions are kink solutions.Furthermore,it is explained that this method can be extended to find kink solutions for other higher-order nonlinear nonintegrable differential equations.

关 键 词：Benney方程 五阶KDV方程 Painleve变换法 扭波解 

分 类 号：O357.41[理学—流体力学]