一般变系数耗散长水波方程的精确解

数学季刊 ›› 2006, Vol. 21 ›› Issue (4): 522-528.

一般变系数耗散长水波方程的精确解

1. Department of Finance,Shanghai TV University 2. Department of Mathematics and Physics,Henan University of Science and Technology

收稿日期:2002-08-06 出版日期:2006-12-30 发布日期:2023-11-20
作者简介:ZHANG Ling-yuan(1963-),mail,native of Dezhou,Shandong,an associate professor of Shang- hai TV University,engages in nonlinear mathematics physics;ZHANG Jin-liang(1966-),mail,native of Nanyang, Henan,an associate professor of Henan University of Science and Technology,engages in nonlinear mathematical physics.
基金资助:
Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)；

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

1. Department of Finance,Shanghai TV University 2. Department of Mathematics and Physics,Henan University of Science and Technology

Received:2002-08-06 Online:2006-12-30 Published:2023-11-20
About author:ZHANG Ling-yuan(1963-),mail,native of Dezhou,Shandong,an associate professor of Shang- hai TV University,engages in nonlinear mathematics physics;ZHANG Jin-liang(1966-),mail,native of Nanyang, Henan,an associate professor of Henan University of Science and Technology,engages in nonlinear mathematical physics.
Supported by:
Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)；

摘要/Abstract

摘要： By using the homogeneous balance principle(HBP),we derive a Backlund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.

关键词: generalized dispersive long wave equation with variable coefhcients;homo-geneous balance principle(HBP);Backlund transformation(BT);single , solitary , solutions, multi-soliton-like solutions;exact solutions

Abstract: By using the homogeneous balance principle(HBP),we derive a Backlund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.

Key words: generalized dispersive long wave equation with variable coefhcients;homo-geneous balance principle(HBP);Backlund transformation(BT);single , solitary , solutions, multi-soliton-like solutions;exact solutions

中图分类号:

O175.2

张令元, 张金良, 王明亮. 一般变系数耗散长水波方程的精确解[J]. 数学季刊, 2006, 21(4): 522-528.

ZHANG Ling-yuan, ZHANG Jin-liang, WANG Ming-liang. Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients [J]. Chinese Quarterly Journal of Mathematics, 2006, 21(4): 522-528.

[1]	李楠, 赵慧燕, 许丽萍. 带有非常数位势的非线性 Choquard 方程正规化基态解[J]. 数学季刊, 2024, 39(3): 250-261.
[2]	赵杰, 吴喜民, 王娟. 重复齐次化问题的强收敛率[J]. 数学季刊, 2024, 39(2): 171-179.
[3]	许娜. 一类次线性基尔霍夫方程基态解的存在性[J]. 数学季刊, 2023, 38(4): 410-414.
[4]	梁艳霞. 带位势的基尔霍夫方程规范解的存在性[J]. 数学季刊, 2023, 38(2): 196-209.
[5]	代兵兵, 张瑞凤. Born-Infeld理论中的多项式函数模型[J]. 数学季刊, 2022, 37(3): 221-236.
[6]	宋雪, 杨赟瑞, 杨璐. 一个三阶 m 点边值问题的三个正解 [J]. 数学季刊, 2021, 36(4): 369-375.
[7]	李振辉, 许丽萍. 一类具有耦合项的 Kirchhoff 型双调和方程组正解的存在性和多解性[J]. 数学季刊, 2021, 36(1): 49-66.
[8]	范俊杰, 李光芳, 套格图桑. 耦合KdV方程组的复合型新解[J]. 数学季刊, 2021, 36(1): 41-48.
[9]	赵包, 杨赟瑞, 马竹艳. 非局部时滞传染病模型的行波解[J]. 数学季刊, 2020, 35(4): 331-343.
[10]	魏含玉, 皮国梅. 广义Kaup-Newell方程的Hamilton结构及其代数几何解[J]. 数学季刊, 2019, 34(2): 209-220.
[11]	王万鹏. 四阶p-Laplacian边值问题正解的存在性[J]. 数学季刊, 2018, 33(4): 377-385.
[12]	杭伟涛, 王超, 李奇, 杨潇. 一类半线性非保守碰撞振子的允许碰撞周期解[J]. 数学季刊, 2018, 33(2): 111-121.
[13]	康周正. 应用（G^’/G²）-展开法求解非线性分数阶微分方程[J]. 数学季刊, 2017, 32(3): 261-270.
[14]	陆海霞. 四阶弹性梁方程特征值问题正解的存在性[J]. 数学季刊, 2017, 32(1): 7-15.
[15]	张申贵. 一类四阶差分系统的多重周期解[J]. 数学季刊, 2016, 31(3): 260-268.