齐次平衡法和浅水波中WBK方程的精确分析解

数学季刊 ›› 2004, Vol. 19 ›› Issue (3): 240-246.

齐次平衡法和浅水波中WBK方程的精确分析解

Department of Mathematics, Bohai University, Jinzhou 121000, China

收稿日期:2002-08-02 出版日期:2004-09-30 发布日期:2024-03-11
作者简介:XIA zhi(1946-),male,native of Jinzhou,Liaoning,an associate professor of Bohai University, engages in mathematics mechanization.
基金资助:
Supported by the National Nature Science Foundation of China(10371070)； Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)；

Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water

Department of Mathematics, Bohai University, Jinzhou 121000, China

Received:2002-08-02 Online:2004-09-30 Published:2024-03-11
About author:XIA zhi(1946-),male,native of Jinzhou,Liaoning,an associate professor of Bohai University, engages in mathematics mechanization.
Supported by:
Supported by the National Nature Science Foundation of China(10371070)； Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)；

摘要/Abstract

摘要： Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan’s, Xie’s and Yan’s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.

关键词: improved , homogenous , balance , method;Backlund , transformation;solitary , wave
solution;multiple , solution;exact , analytical , solution;rational , solution

Abstract: Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan’s, Xie’s and Yan’s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.

Key words: improved , homogenous , balance , method;Backlund , transformation;solitary , wave
solution;multiple , solution;exact , analytical , solution;rational , solution

中图分类号:

O175.29

夏志. 齐次平衡法和浅水波中WBK方程的精确分析解[J]. 数学季刊, 2004, 19(3): 240-246.

XIA Zhi . Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(3): 240-246.