Rosenau方程的显式行波解及动力学行为  

Explicit travelling wave solutions and dynamic behaviors of the Rosenau equation

作　　者：林府标 杨欣霞 张千宏[1] Lin Fubiao;Yang Xinxia;Zhang Qianhong(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数统与统计学院,贵阳550025

出　　处：《河南师范大学学报（自然科学版）》2024年第2期33-40,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11761018);贵州省科技计划基金项目(黔科合基础-ZK[2022]一般021);黔科合平台人才-GCC[2022]020-1;贵州省高等学校系统建模与数据挖掘重点实验室课题(2023013)。

摘　　要：找到Rosenau方程的显式精确解十分困难,研究方法常采用数值离散求解技术.首先,采用李群分析法给出了Rosenau方程的对称群、约化常微分方程和群不变解;其次,构造了一种精确求解非线性偏微分方程的exp(-φ(ξ))展式法,利用此方法找到了Rosenau方程的显式行波解,分析了解的动力学行为;最后,所获得的显式行波解既证明了Rosenau方程显式精确解的存在性,又可用于验证数值解的精度、检验数值离散方案的优劣,为工程领域的实际应用提供理论依据和参考.It is typically difficult to obtain explicit exact solutions of the Rosenau equation,it was usually intensively investigated by use of the numerical schemes and techniques.Firstly,symmetric groups,reduced ordinary differential equations and group invariant solutions of the Rosenau equation were given by the method of classical Lie group analysis.Secondly,an exp(-φ(ξ))-expansion method for solving analytically nonlinear partial differential equation was constructed.Moreover,explicit travelling wave solutions of the Rosenau equation were found by using the exp(-φ(ξ))-expansion method,the corresponding dynamic behaviors of solutions were also analyzed.Finally,on the one hand,the existence of solutions of the Rosenau equation was demonstrated by these obtained explicit travelling wave solutions.These obtained exact solutions can be used to verify accuracy of numerical solution,test advantages and disadvantages of numerical discrete scheme,and study dynamic behaviors of solutions.In addition,it also provides a theoretical basis for the practical application in the field of engineering.

关 键 词：Rosenau方程 显式行波解 动力学行为 

分 类 号：O175.4[理学—数学] O175.29[理学—基础数学]