## 留言板

Camassa-Holm方程凹凸尖峰及光滑孤立子解

 引用本文: 田立新, 许刚, 刘曾荣. Camassa-Holm方程凹凸尖峰及光滑孤立子解[J]. 应用数学和力学, 2002, 23(5): 497-506.
TIAN Li-xin, XU Gang, LIU Zeng-rong. The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2002, 23(5): 497-506.
 Citation: TIAN Li-xin, XU Gang, LIU Zeng-rong. The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2002, 23(5): 497-506.

## Camassa-Holm方程凹凸尖峰及光滑孤立子解

###### 作者简介:田立新(1963- ),男,江苏人,教授,博士.
• 中图分类号: O175.29

## The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation

• 摘要: 研究一类完全可积的新型浅水波方程Camassa-Holm方程的行波孤立子解及双孤立子解.引入凹凸尖峰孤立子及光滑孤立子的概念,研究得到该方程的行波解中具有尖峰性质的凹凸尖峰孤立子解及光滑孤立子解.同时利用Backlund变换给出该类方程的新的双孤立子解.
•  [1] Roberto Camassa,Darryl D Holm.An integrable shallow water equation with peaked solitons[J].Phy Rev Letters,1993,71(13):1661-1664. [2] Alber M S,Camassa R.The geometry of peaked soliton and billiard solutions of a class of integrable PDE's[J].Letters Math Phy,1994,32(2):137-151. [3] Clarkson P A,Mansfield E L,Priestley T J.Symmetries of a class of nonlinear third-order partial differential equations[J].Math Comput Modelling,1997,25(8/9):195-212. [4] XIN Zhou-ping,ZHANG Ping.On the weak solutions to a shallow water equation[J].Comm Pure Appli Math,2000,53(9):1411-1433. [5] Michael Fisher,Jeremy Schiff.The camassa Holm equation:Conserved quantities and the initial value problem[J].Phy Lett A,1999,259(3):371-376. [6] Adrian Constantin,Waner A Atrauss.Stability of peakons[J].Comm Pure Appli Math,2000,53(10):603-610. [7] Adrian Constantin,Joachim Escher.Well-posedness,global existence and blown up phenomena for a periodic quasi-linear hyperbolic equation[J].1998,51(5):475-504. [8] TIAN Li-xin.Wavelet approximate inertial manifold in nonlinear solitary wave equation[J].J Math Phy,2000,41(8):5773-5793. [9] TIAN Li-xin,LIU Zeng-rong.P dissipative operator[J].Comm Math Phy,1999,201(3):509-538. [10] TIAN Li-xin,LIU Zeng-rong.The Schrdinger operator[J].Proc Amer Math Soc,1998,126(1):201-211.
##### 计量
• 文章访问数:  2658
• HTML全文浏览量:  168
• PDF下载量:  736
• 被引次数: 0
##### 出版历程
• 收稿日期:  2001-08-20
• 修回日期:  2001-11-28
• 刊出日期:  2002-05-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈