| 广义Davey-Stewartson系统驻波的强不稳定性 |
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| 引用本文： | 李晓光,张健,岳仲涛. 广义Davey-Stewartson系统驻波的强不稳定性[J]. 数学学报, 2018, 61(3): 375-382 |
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| 作者姓名： | 李晓光 张健 岳仲涛 |
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| 作者单位： | 1.四川师范大学经济与管理学院 成都 610068;2.四川师范大学数学与软件科学学院 成都 610068;3.电子科技大学数学科学学院 成都 611731;4.电子科技大学基础与前沿研究学院 成都 610054 |
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| 基金项目： | 国家自然科学基金资助项目（11371267，11771314）；教育部科学技术研究重点项目（211162）；四川省青年基金资助项目（2012JQ0011） |
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| 摘 要： | 本文研究方程驻波的强不稳定性iu_t+△u+a|u|~(p-1)u+E_1(|u|~2)u=0,t≥0,x∈R~n,其中a0,1p(n+2)/(n+2)~+,n∈{2,3}.当1+4/n≤pn+2/(n-2)~+)时,文[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system,Commun.Math.Phys.,2008,283:93-125]在驻波的频率满足一定假设条件下,证明了此方程驻波的强不稳定性.本文去掉这个假设,得到相同的结论.
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Instability for the Standing Wave of Generalized Davey-Stewartson Equation |
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| Xiao Guang LI,Jian ZHANG,Zhong Tao YUE. Instability for the Standing Wave of Generalized Davey-Stewartson Equation[J]. Acta Mathematica Sinica, 2018, 61(3): 375-382 |
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| Authors: | Xiao Guang LI Jian ZHANG Zhong Tao YUE |
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| Affiliation: | 1.College of Economics and Management, Sichuan Normal University, Chengdu 610068, P. R. China;2.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P. R. China;3.School of Mathematical Sciences, UESTC, Chengdu 611731, P. R. China;4.Institute of Fundamental and Frontier Sciences, UESTC, Chengdu 610054, P. R. China |
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| Abstract: | The aim of this paper is to study the standing wave of the generalized Davey-Stewartson equation iut+Δu+a|u|p-1u+E1(|u|2)u=0, t ≥ 0,x∈Rn, where a,b > 0, 1 < p < (n-2)/((n+2)+), n∈{2,3}. When 1+4/n ≤ p < (n-2)/((n+2)+),[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system, Commun. Math. Phys., 2008, 283:93-125], under an assumption about the frequency of the standing wave, obtained the strongly instability of the ground state standing waves. In the present paper, We establish the same conclusion without that assumption. |
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| Keywords: | Davey-Stewartson equation standing wave instability |
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