| 一类Boussinesq方程的同宿轨和周期孤立子 |
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| 引用本文： | 李正彪,戴正德.一类Boussinesq方程的同宿轨和周期孤立子[J].吉首大学学报(自然科学版),2005,26(2):1-4. |
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| 作者姓名： | 李正彪 戴正德 |
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| 作者单位： | 云南大学数理学院,云南,昆明,650091;曲靖师范学院数学系,云南,曲靖,655000;云南大学数理学院,云南,昆明,650091 |
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| 基金项目： | Supported by National Natural Science Foundation of China（10361007） and National Natural Science Foundation of Yurman Province（2004A0001M） |
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| 摘 要： | 研究了一类具有周期边界条件和偶约束的Boussinesq方程.首先，通过线性稳定性分析，证明了“坏”Boussinesq方程存在同宿轨解,而“好”Boussinesq方程存在孤立子解.然后，利用Hirota双线性方法，分别获得了同宿轨和孤立子的显式表达式，而且发现孤立子解存在爆破现象.
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| 关 键 词： | Boussinesq方程 同宿轨 周期孤立子 |
| 文章编号： | 1007-2985（2005）02-0001-04 |
| 收稿时间： | 2005-02-23 |
| 修稿时间： | 2005-02-23 |
Homoclinic Orbits and Periodic Solitons for a Class of Boussinesq Equations |
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| LI Zheng-biao,DAI Zheng-de.Homoclinic Orbits and Periodic Solitons for a Class of Boussinesq Equations[J].Journal of Jishou University(Natural Science Edition),2005,26(2):1-4. |
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| Authors: | LI Zheng-biao DAI Zheng-de |
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| Institution: | (1.School of Mathematics and Physics,Yunnan University,Kunming 650091,Yunan China; 2.Department of Mathematics,Qujing Teachers College,Qujing 655000,Yunan China) |
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| Abstract: | This paper considers homoclinic orbits and periodic solitons for a class of Boussinesq equations with periodic boundary condition and even constraint condition.At first,by the linearized stability analysis,the authors get the existence of homoclinic orbits for "bad" Bq equation and periodic solitons for "good" Bq equation.Then,by the Hirota's bilinear method,the exact expressions of homoclinic orbits and periodic solitons are obtained respectively,and the authors find there is blow-up phenomenon for the soliton solutions. |
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| Keywords: | Boussinesq equation homoclinic orbit periodic soliton |
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