KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | JOURNAL OF MATHEMATICAL PHYSICS |
ISSN | 0022-2488 |
Volume | 60Issue:8Pages:47 |
Abstract | In 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. |
DOI | 10.1063/1.5058722 |
Language | 英语 |
Funding Project | NSFC[11731014] ; NSFC[11571346] ; CAS Interdisciplinary Innovation Team |
WOS Research Area | Physics |
WOS Subject | Physics, Mathematical |
WOS ID | WOS:000483885000008 |
Publisher | AMER INST PHYSICS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35671 |
Collection | 系统科学研究所 |
Corresponding Author | Yan, Zhenya |
Affiliation | 1.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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