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| 一类非线性Boussinesq方程的有界行波解 | |
| 引用本文： | 谢绍龙,高斌,洪晓春.一类非线性Boussinesq方程的有界行波解[J].湖南师范大学自然科学学报,2006,29(3):18-22. |
| 作者姓名： | 谢绍龙 高斌 洪晓春 |
| 作者单位： | 1. 玉溪师范学院数学系,中国,玉溪,653100 2. 玉溪师范学院物理系,中国,玉溪,653100 3. 曲靖师范学院初教系,中国,曲靖,655000 |
| 基金项目： | 国家自然科学基金资助项目(10261008) |
| 摘 要： | 用微分方程定性理论结合数值模拟方法研究了一类非线性Boussinesq方程的有界行波.在r>0的条件下,首先把Boussinesq方程转换成一个常微平面系统.然后用定性理论讨论该平面系统的奇点性质,得到了该系统的相图分支,根据相图给出了有界行波的存在条件,并求出了有界行波的解.最后用数学软件Maple对行波方程进行数值模拟,得到了有界行波的平面模拟图.数值模拟和理论分析结果是一致的. |
| 关 键 词： | 非线性Boussinesq方程 有界行波 周期轨 同宿轨 |
| 文章编号： | 1000-2537（2006）03-0018-05 |
| 收稿时间： | 2005-12-20 |
| 修稿时间： | 2005年12月20 |
Bounded Traveling Waves of a Nonlinear Boussinesq Equation |
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| XIE Shao-long,GAO Bin,HONG Xiao-chun.Bounded Traveling Waves of a Nonlinear Boussinesq Equation[J].Journal of Natural Science of Hunan Normal University,2006,29(3):18-22. | |
| Authors: | XIE Shao-long GAO Bin HONG Xiao-chun |
| Institution: | 1. Department of Mathematics, Yuxi Normal College, Yuxi 653100, China; 2. Department of Physles, Yuxi Normal College, Yuxi 653100,China; 3. Primary Education Department, Qujing Teachers College, Qujing 655000, China |
| Abstract: | The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the bounded traveling waves of a nonlinear Boussinesq equation.Under the condition r>0,the Boussinesq equation is changed to a planar system,the proprties of the singular points are studied and the bifurcation phase portraits are drew.The parameter conditions that the bounded traveling waves appear are found,and their solutions are obtained.Finally,the planar graphs of the traveling wave equation are simulated by use mathematical software Maple.The numerical simulation and qualitative results are identical. |
| Keywords: | nonlinear Boussinesq equation bounded traveling wave periodic orbit homoclinic orbit |
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