| (2+1)维KD方程的解及分岔行为 |
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| 引用本文： | 温纪云,符文彬,黄琼伟,杨先林.(2+1)维KD方程的解及分岔行为[J].动力学与控制学报,2011,9(1):40-43. |
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| 作者姓名： | 温纪云 符文彬 黄琼伟 杨先林 |
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| 作者单位： | 湖南大学机械与运载工程学院,长沙 410082;湖南大学机械与运载工程学院,长沙 410082;湖南大学机械与运载工程学院,长沙 410082;湖南广播电视大学理工教学部,长沙 410004 |
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| 基金项目： | 湖南省科学技术厅科技计划资助项目(2009FJ3077) |
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| 摘 要： | 通过行波变换,将非线性偏微分方程化为常微分方程,利用辅助常微分方程的解来构造偏微分方程的精确解,获得了(2+1)维Konopelchenko-Dubrovsky方程的孤波解和周期解.然后直接研究变换以后的常微分方程,揭示该方程控制的动力系统的鞍结分岔行为,画出了系统的分岔图.
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| 关 键 词： | 非线性偏微分方程 行波变换 精确解 分岔 |
| 收稿时间： | 2010/10/18 0:00:00 |
| 修稿时间： | 2011/1/18 0:00:00 |
Exact solution and bifurcation for (2+1) dimensional KD equation |
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| Wen Jiyun,Fu Wenbin,Huang Qiongwei and Yang Xianlin.Exact solution and bifurcation for (2+1) dimensional KD equation[J].Journal of Dynamics and Control,2011,9(1):40-43. |
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| Authors: | Wen Jiyun Fu Wenbin Huang Qiongwei and Yang Xianlin |
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| Affiliation: | Wen Jiyun1 Fu Wenbin1 Huang Qiongwei1 Yang Xianlin2 (1.College of Mechanical and Vehicle Engineering,HNU,Changsha 410082,China) (2.Hunan Radio and Television University,Changsha 410004,China) |
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| Abstract: | By means of the traveling wave transformation nonlinear partial differential equations are reduced to ordinary differential equations. Applying solutions of the ordinary differential equation, we have constructed exact solutions of nonlinear partial differential equations and have obtained some exact solitary wave solutions and periodic solutions for the (2+1) dimensional Konopelchenko-Dubrovsky equation. The ordinary differential equation is directly studied and a bifurcation diagram of the system is drew. The saddle-node bifurcation which leads to jump and hysteresis is analyzed. |
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| Keywords: | nonlinear partial differential equation wave transformation exact solution bifurcation |
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