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一类广义四阶非线性Camassa-Holm方程的行波解 被引量：3

TRAVELLING WAVE SOLUTIONS IN A CLASS OF NONLINEAR FOURTH ORDER VARIANT OF A GENERALIZED CAMASSA-HOLM EQUATION
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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. 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.
作者 唐亚宁 徐伟
机构地区 西北工业大学理学院数学系 西北工业大学网络与教育技术中心
出处 《系统科学与数学》 CSCD 北大核心 2008年第2期180-192,共13页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(10332030，10472091)资助课题
关键词 广义的四阶非线性Camassa-Holm方程 孤立波解 周期波解 波的不光滑性 分支理论 Camassa-Holm equation, solitary wave solutions, periodic wave solutions, non-smooth wave, bifurcation theory.
分类号 O175.29 [理学—基础数学] O175.8 [理学—基础数学]
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共引文献37

同被引文献19

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  • 9Hakkaev S and Kirchev K. Local well-posedned and orbital stability of solitary wave solutions for the generalized Camassa-Holm equation. Comm. in Partial Diff. Eq., 2005, 30: 761-781.
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系统科学与数学
2008年 第2期

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