| Four types of bounded wave solutions of CH-γ equation |
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| 作者单位： | Min-ying TANG（School of Mathematical Sciences and Center for Nonlinear Science Studies, South China University of Technology, Guangzhou 510640, China） ;
Wen-ling ZHANG（Department of Mathematics and Physics, National Natural Science Foundation of China, Beijing 100085,China） ; |
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| 基金项目： | This work was supported by the National Natural Science Foundation of China (Grant No. 10571062) |
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| 摘 要： | Recently, many authors have studied the following CH-γ equationut c0ux 3uux - α2(uxxt uuxxx 2uxuxx) γuxxx =0,where α2, c0 and γ are paramters. Its bounded wave solutions have been investigated mainly for the case α2 ＞ 0. For the case α2 ＜ 0, the existence of three bounded waves (regular solitary waves,compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given.In this paper, not only the existence of four types of bounded waves periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the case α2 ＜ 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.
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| 关 键 词： | CH-γ equation bounded waves explicit expressions implicit expressions. |
| 收稿时间： | 29 November 2005 |
| 修稿时间： | 14 July 2006 |
Four types of bounded wave solutions of CH-γ equation |
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| Authors: | Min-ying Tang and Wen-ling Zhang |
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| Institution: | (1) School of Mathematical Sciences and Center for Nonlinear Science Studies, South China University of Technology, Guangzhou, 510640, China;(2) Department of Mathematics and Physics, National Natural Science Foundation of China, Beijing, 100085, China |
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| Abstract: | Recently, many authors have studied the following CH-γ equation: u
t
+ c
0
u
x
+ 3uu
x
− α
2(u
xxt
+ uu
xxx
+ 2u
x
u
xx
) + γu
xxx
= 0, where α
2, c
0 and γ are parameters. Its bounded wave solutions have been investigated mainly for the case α
2 > 0. For the case α
2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin
et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves,
compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions
are given for the case α
2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of
our results.
This work was supported by the National Natural Science Foundation of China (Grant No. 10571062) |
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| Keywords: | CH-γ equation bounded waves explicit expressions implicit expressions |
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