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非线性自治振动系统同宿解的广义双曲函数摄动法

陈洋洋 燕乐纬 佘锦炎 陈树辉

陈洋洋, 燕乐纬, 佘锦炎, 陈树辉. 非线性自治振动系统同宿解的广义双曲函数摄动法[J]. 应用数学和力学, 2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004
引用本文: 陈洋洋, 燕乐纬, 佘锦炎, 陈树辉. 非线性自治振动系统同宿解的广义双曲函数摄动法[J]. 应用数学和力学, 2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004
CHEN Yang-yang, YAN Le-wei, SZE Kam-yim, CHEN Shu-hui. Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004
Citation: CHEN Yang-yang, YAN Le-wei, SZE Kam-yim, CHEN Shu-hui. Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004

非线性自治振动系统同宿解的广义双曲函数摄动法

doi: 10.3879/j.issn.1000-0887.2012.09.004
基金项目: 国家自然科学基金资助项目(10972240);国家自然科学青年基金资助项目(11102045);广东省自然科学博士启动基金资助项目(S2011040004039);广东省高校优秀青年创新人才培育基金资助项目(LYM10108);广州市高校科研基金资助项目(10A024);香港研究资助局研究基金资助项目(GRF HKU 7173 09E)
详细信息
    通讯作者:

    陈洋洋(1981—), 男, 广东人, 讲师, 博士 (联系人. Tel:+86-20-86395053; E-mail:chenyangyang2007@gmail.com).

  • 中图分类号: O322

Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems

  • 摘要: 提出广义的双曲函数摄动法,用于求解强非线性自治振子的同宿解,克服一般摄动步骤中派生方程须存在显式精确同宿解的限制.以广义双曲函数作为摄动步骤的基本函数,拓展了基于双曲函数的摄动法的适用范围.对同时含2,3次和含4次强非线性项的系统进行求解分析,验证了方法的有效性和精度.
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出版历程
  • 收稿日期:  2012-05-08
  • 修回日期:  2012-05-16
  • 刊出日期:  2012-09-15

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