An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval

doi:10.1093/imamat/hxab007

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	An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval
	Yan, Zhenya 1,2
	2021-06-01
发表期刊	IMA JOURNAL OF APPLIED MATHEMATICS
ISSN	0272-4960
卷号	86 期号:3 页码:427-489
摘要	The general three-component nonlinear Schrodinger (gtc-NLS) equations are completely integrable and contain the self-focusing, defocusing and mixed cases, which are applied in many physical fields. In this paper, we would like to use the Fokas method to explore the initial-boundary value (IBV) problem for the gtc-NLS equations with a 4 x 4 matrix Lax pair on a finite interval based on the inverse scattering transform. The solutions of the gtc-NLS equations can be expressed using the solution of a 4 x 4 matrix Riemann-Hilbert (RH) problem constructed in the complex k-plane. The jump matrices of the RH problem can be explicitly found in terms of three spectral functions related to the initial data, and the Dirichlet-Neumann boundary data, respectively. The global relation between the distinct spectral functions is also proposed to derive two distinct but equivalent types of representations of the Dirichlet-Neumann boundary value problems. Particularly, the relevant formulae for the boundary value problems on the finite interval can generate ones on the half-line as the length of the interval closes to infinity. Finally, we also analyse the linearizable boundary conditions for the Gel' fand-Levitan-Marchenko representation. These results will be useful to further study the solution properties of the IBV problem of the gtc-NLS system by using the Deift-Zhou's nonlinear steepest descent method and some numerical methods.
关键词	general three-component nonlinear Schrodinger equations initial-boundary value problem inverse scattering Riemann-Hilbert problem global relation Dirichlet and Neumann problems Gel'fand-Levitan-Marchenko representation
DOI	10.1093/imamat/hxab007
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11925108] ; National Natural Science Foundation of China[11731014]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000670952800001
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58912
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Zhenya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Yan, Zhenya. An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval[J]. IMA JOURNAL OF APPLIED MATHEMATICS,2021,86(3):427-489.
APA	Yan, Zhenya.(2021).An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval.IMA JOURNAL OF APPLIED MATHEMATICS,86(3),427-489.
MLA	Yan, Zhenya."An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval".IMA JOURNAL OF APPLIED MATHEMATICS 86.3(2021):427-489.