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Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 x 4 Lax pair on a finite interval
Yan, Zhenya1,2
2019-08-01
Source PublicationJOURNAL OF MATHEMATICAL PHYSICS
ISSN0022-2488
Volume60Issue:8Pages:47
AbstractIn this paper, we explore the initial-boundary value (IBV) problem for an integrable spin-1 Gross-Pitaevskii system with a 4 x 4 Lax pair on the finite interval x is an element of [0, L] by extending the Fokas unified approach. The solution of this three-component system can be expressed by means of the solution of a 4 x 4 matrix Riemann-Hilbert (RH) problem formulated in the complex spectral k-plane. Furthermore, the relevant jump matrices with explicit (x, t)-dependence of the matrix RH problem can be explicitly obtained using three spectral functions {s(k), S(k), S-L(k)} arising from the initial data and Dirichlet-Neumann boundary conditions at x = 0, L, respectively. The global relation is also presented and used to deduce two distinct but equivalent types of representations [i.e., one via the large k of asymptotics of the eigenfunctions and another one in terms of the Gel'fand-Levitan-Marchenko (GLM) approach] for the Dirichlet and Neumann boundary value problems. In particular, the formulae for IBV problem on the finite interval can be extended to the ones on a half-line as the length L of the interval approaches to infinity. Moreover, we also give the linearizable boundary conditions for the GLM representations.
DOI10.1063/1.5058722
Language英语
Funding ProjectNSFC[11731014] ; NSFC[11571346] ; CAS Interdisciplinary Innovation Team
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000483885000008
PublisherAMER INST PHYSICS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35671
Collection系统科学研究所
Corresponding AuthorYan, Zhenya
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Yan, Zhenya. Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 x 4 Lax pair on a finite interval[J]. JOURNAL OF MATHEMATICAL PHYSICS,2019,60(8):47.
APA Yan, Zhenya.(2019).Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 x 4 Lax pair on a finite interval.JOURNAL OF MATHEMATICAL PHYSICS,60(8),47.
MLA Yan, Zhenya."Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 x 4 Lax pair on a finite interval".JOURNAL OF MATHEMATICAL PHYSICS 60.8(2019):47.
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