广义Davey——Stewartson系统驻波的强不稳定性

李晓光, 张健, 岳仲涛

数学学报 ›› 2018, Vol. 61 ›› Issue (3) : 375-382.

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数学学报 ›› 2018, Vol. 61 ›› Issue (3) : 375-382. DOI: 10.12386/A2018sxxb0032
论文

广义Davey——Stewartson系统驻波的强不稳定性

    李晓光1, 张健2,3, 岳仲涛3,4
作者信息 +

Instability for the Standing Wave of Generalized Davey-Stewartson Equation

    Xiao Guang LI1, Jian ZHANG2,3, Zhong Tao YUE3,4
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文章历史 +

摘要

本文研究方程驻波的强不稳定性iutu+a|u|p-1u+E1(|u|2u=0,t≥0,x∈Rn,其中a > 0,1 < p <(n-2)/((n+2)+),n∈{2,3}.当1+4/np <(n-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.

Abstract

The aim of this paper is to study the standing wave of the generalized Davey-Stewartson equation iutu+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/np < (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.

关键词

Davey-Stewartson系统 / 驻波 / 强不稳定

Key words

Davey-Stewartson equation / standing wave / instability

引用本文

导出引用
李晓光, 张健, 岳仲涛. 广义Davey——Stewartson系统驻波的强不稳定性. 数学学报, 2018, 61(3): 375-382 https://doi.org/10.12386/A2018sxxb0032
Xiao Guang LI, Jian ZHANG, Zhong Tao YUE. Instability for the Standing Wave of Generalized Davey-Stewartson Equation. Acta Mathematica Sinica, Chinese Series, 2018, 61(3): 375-382 https://doi.org/10.12386/A2018sxxb0032

参考文献

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基金

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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