| 一类广义四阶非线性Camassa-Holm方程的行波解 |
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| 引用本文： | 唐亚宁,徐伟.一类广义四阶非线性Camassa-Holm方程的行波解[J].系统科学与数学,2008,28(2):180-192. |
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| 作者姓名： | 唐亚宁 徐伟 |
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| 作者单位： | 1. 西北工业大学理学院数学系,西安,710072
2. 西北工业大学理学院数学系,西安,710072;西北工业大学网络与教育技术中心,西安,710072 |
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| 摘 要： | 用动力系统的分支理论研究了一类广义四阶非线性Camassa-Holm方程的动力学行为和行波解,发现方程存在一些孤立波解,周期波解和一些诸如Compacton类型的非光滑行波解.在不同的参数条件下,给出了这些解存在的条件和一些特殊条件下的精确解.
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| 关 键 词： | 广义的四阶非线性Camasse-Holm方程 孤立波解 周期波解 波的不光滑性 分支理论 一类广义 四阶 非线性 方程 行波解 EQUATION GENERALIZED VARIANT ORDER NONLINEAR CLASS SOLUTIONS 精确解 特殊条件 参数 非光滑 类型 Compacton 周期波解 孤立波解 |
| 收稿时间： | 2005-6-10 |
| 修稿时间： | 2005年6月10日 |
Travelling Wave Solutions in a Class of Nonlinear Fourth Order Variant of a Generalized Camassa-Holm Equation |
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| TANG Yaning,XU Wei.Travelling Wave Solutions in a Class of Nonlinear Fourth Order Variant of a Generalized Camassa-Holm Equation[J].Journal of Systems Science and Mathematical Sciences,2008,28(2):180-192. |
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| Authors: | TANG Yaning XU Wei |
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| Institution: | (1)Department of Applied Mathematics, School of Science, Northwestern polytechnical university, xi'an710072;(2)Network Education Technology center, Northwestern polytechnical university, xi'an710072 |
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| Abstract: | By using the bifurcation theory of dynamical systems, it is shown that there exist smooth solitary wave solutions, periodic wave solutions and non-smooth solutions such as compactons for a class of generalized nonlinear fourth order Camassa-Holm equation. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given, and some exact solutions under some special conditions are obtained. |
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| Keywords: | Camassa-Holm equation solitary wave solutions periodic wave solutions non-smooth wave bifurcation theory |
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