耦合KdV和Schwarzian KdV方程的显式行波解

数学季刊 ›› 2012, Vol. 27 ›› Issue (3): 371-374.

耦合KdV和Schwarzian KdV方程的显式行波解

College of Mathematics and Statistics, Henan University of Science and Technology

收稿日期:2010-11-05 出版日期:2012-09-30 发布日期:2023-03-22
通讯作者: LI Ling-xiao(corresponding author)(1976-), female, native of Luoyang, Henan, a lecturer of Henan University of Science and Technology, M.S.D., engages in nonlinear science.
作者简介:LI Ling-xiao(corresponding author)(1976-), female, native of Luoyang, Henan, a lecturer of Henan University of Science and Technology, M.S.D., engages in nonlinear science.
基金资助:
Supported by the Natural Science Foundation of Education Department of Henan Province(2011B110013)；Supported by the Youth Science Foundation of Henan University of Scienceand Technology(2008QN026)

Exact Travelling Wave Solutions for a Combined KdV and Schwarzian KdV Equation

College of Mathematics and Statistics, Henan University of Science and Technology

Received:2010-11-05 Online:2012-09-30 Published:2023-03-22
Contact: LI Ling-xiao(corresponding author)(1976-), female, native of Luoyang, Henan, a lecturer of Henan University of Science and Technology, M.S.D., engages in nonlinear science.
About author:LI Ling-xiao(corresponding author)(1976-), female, native of Luoyang, Henan, a lecturer of Henan University of Science and Technology, M.S.D., engages in nonlinear science.
Supported by:
Supported by the Natural Science Foundation of Education Department of Henan Province(2011B110013)；Supported by the Youth Science Foundation of Henan University of Scienceand Technology(2008QN026)

摘要/Abstract

摘要： In this paper the (G’/G)-expansion method is used to find exact travelling wave solutions for a combined KdV and Schwarzian KdV equation. As a result, multiple travelling wave solutions with arbitrary parameters are obtained, which are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are derived from the travelling waves. The (G’/G)-expansion method presents a wider applicability for handling nonlinear wave equations.

关键词: the (G’/G)-expansion method, travelling wave solutions, homogeneous balance, the combined KdV and Schwarzian KdV equation

Abstract: In this paper the (G’/G)-expansion method is used to find exact travelling wave solutions for a combined KdV and Schwarzian KdV equation. As a result, multiple travelling wave solutions with arbitrary parameters are obtained, which are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are derived from the travelling waves. The (G’/G)-expansion method presents a wider applicability for handling nonlinear wave equations.

Key words: the (G’/G)-expansion method, travelling wave solutions, homogeneous balance, the combined KdV and Schwarzian KdV equatio

中图分类号:

O175.2

李灵晓, 李二强. 耦合KdV和Schwarzian KdV方程的显式行波解[J]. 数学季刊, 2012, 27(3): 371-374.

LI Ling-xiao, LI Er-qiang. Exact Travelling Wave Solutions for a Combined KdV and Schwarzian KdV Equation[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(3): 371-374.

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[2]	王秀梅, 朱跃峰. 广度kdv方程的精确解:改进的齐次平衡法[J]. 数学季刊, 2008, 23(2): 260-269.