一类非线性浅水波方程的对称动态分析和精确解  

Symmetrical Dynamic Analysis and Exact Solutions of a Class of Nonlinear Shallow Water Wave Equations

作　　者：康晓蓉[1] 鲜大权[1] 鲜骊珠 KANG Xiaorong;XIAN Daquan;XIAN Lizhu(School of Sciences,Southwest University of Science and Technology,Mianyang 621010 China;Chengdu University of Technology Sino-British Collaborative Education,Chengdu 610059 China)

机构地区：[1]西南科技大学理学院,四川绵阳621010 [2]成都理工大学中英合作办学,四川成都610059

出　　处：《西华大学学报（自然科学版）》2021年第6期103-108,共6页Journal of Xihua University:Natural Science Edition

基　　金：西南科技大学教改项目(19xn0040)。

摘　　要：运用李群分析法得到一类非线性浅水波方程的李点对称约化方程,应用截断幂级数展开法求解约化方程,得到方程新的非行波精确解,并讨论解的局域演化特征及几何结构。The Lie group analysis method is used to obtain Lie point symmetry reduced equations for a class of nonlinear shallow water wave equations, and the truncated power series expansion method is also used to solve the reduced equation. Some new non-traveling wave exact solutions are obtained, and the local evolution characteristics and geometric structure of a certain solution are discussed.

关 键 词：非线性浅水波方程 李群分析 截断幂级数展开法 精确解 局域演化特征 

分 类 号：O241.6[理学—计算数学]