An initial-boundary value problem for the general three-component nonlinear Schrodinger equations on a finite interval
文献类型：期刊论文
| 作者 | Yan, Zhenya1,2 |
| 刊名 | IMA JOURNAL OF APPLIED MATHEMATICS
 |
| 出版日期 | 2021-06-01 |
| 卷号 | 86期号:3页码:427-489 |
| 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 |
| ISSN号 | 0272-4960 |
| DOI | 10.1093/imamat/hxab007 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11925108] ; National Natural Science Foundation of China[11731014] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000670952800001 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58911]  |
| 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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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