| 修正Camassa-Holm方程尖峰孤波解的稳定性 |
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| 引用本文： | 刘小华,张卫国. 修正Camassa-Holm方程尖峰孤波解的稳定性[J]. 生物数学学报, 2011, 0(3): 517-523 |
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| 作者姓名： | 刘小华 张卫国 |
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| 作者单位： | 上海理工大学理学院;贵州民族学院理学院; |
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| 基金项目： | 国家自然科学基金项目(编号:11071164); 上海市自然科学基金项目(编号:10ZR1420800); 上海市重点学科建设项目(编号:S30501) |
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| 摘 要： | 通过对具有哈密顿结构的修正Camassa-Holm方程的三个守恒量进行先验估计,算子谱分析,讨论了尖峰孤波解的稳定性取决于d″（c）的符号,并且给出d″（c）的具体表达式.借此给出修正Camassa-Holm方程的尖峰孤波解的稳定性与速度c有关,即c〉0,孤波解稳定,c〈0,孤波解不稳定;推广了[2]中相应的结论.
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| 关 键 词： | Camassa-Holm方程 尖峰孤立波 稳定性 |
Stability of Peakons to the Modified Camassa-Holm Equation |
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| LIU Xiao-hua ZHANG Wei-guo. Stability of Peakons to the Modified Camassa-Holm Equation[J]. Journal of Biomathematics, 2011, 0(3): 517-523 |
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| Authors: | LIU Xiao-hua ZHANG Wei-guo |
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| Affiliation: | LIU Xiao-hua~(1,2) ZHANG Wei-guo~1 (1 Business School of University of Shanghai for Science and Technology,Shanghai 200093 China) (2 Business School of University of Guizhou for Nationalities,Guizhou Guiyang 550025 China) |
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| Abstract: | The modified Camassa-Holm equation is a Hamiltonian system,we estimate its conserved quantities,and ananlyze the operator spectrum.the stability of peakons depend on the sign of d(c),which is expressed exactly.As a result,we know that the stabiltiy is related to velocity c,when c>0 holds,the peakon is stable,c<0 holds,the peakon is unstable.This conclusion improve the same result of A.Constantin[2]. |
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| Keywords: | Nonlinear Klein-Gordon equation Solitary wave solution Stability |
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