Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations

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	Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations
	Cao, Daomin1 ; Noussair, Ezzat S.2; Yan, Shusen 3
	2008
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	360 期号:7 页码:3813-3837
摘要	In this paper we study the existence and qualitative property of standing wave solutions psi(x, t) = e- iEt/hu(x) for the nonlinear Schrodinger equation i h partial derivative psi/partial derivative t + h(2)/2m Delta psi-W(x)(psi)+vertical bar psi vertical bar(p-1)psi=02m.. with E being a critical frequency in the sense that inf x. RN W( x) = E. We show that if the zero set of V = W - E has k isolated connected components Z(i)( i = 1, center dot center dot center dot, k) such that the interior of Zi is not empty and. Zi is smooth, V has t isolated zero points, b(i), i = 1, center dot center dot center dot, t, and V has l critical points a(i)( i = 1, center dot center dot center dot, l) such that V (a(i)) > 0, then for h > 0 small, there exists a standing wave solution which is trapped in a neighborhood of boolean OR(i=1) Z(i) boolean OR(boolean OR(t)(i)(= 1){b(i)})boolean OR(boolean OR(l)(i)(= 1){a(i)} ). Moreover the amplitudes of the standing wave around boolean OR(k)(i)(=1) Z(i), boolean OR(t)(i)(=1){b(i)} and boolean OR(l)(i)(=1){a(i)} are of a different order of h. This type of multi- scale solution has never before been obtained.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000254589400018
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6593
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia 3.Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia
推荐引用方式 GB/T 7714	Cao, Daomin,Noussair, Ezzat S.,Yan, Shusen. Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2008,360(7):3813-3837.
APA	Cao, Daomin,Noussair, Ezzat S.,&Yan, Shusen.(2008).Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,360(7),3813-3837.
MLA	Cao, Daomin,et al."Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 360.7(2008):3813-3837.