KMS Of Academy of mathematics and systems sciences, CAS
| Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions | |
Zhang, Guoqiang1; Chen, Shuyan2,3; Yan, Zhenya2,3
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| 2020 | |
| Source Publication | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
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| ISSN | 1007-5704 |
| Volume | 80Pages:22 |
| Abstract | In this paper, we investigate the inverse scattering transforms and soliton solutions of both focusing and defocusing Hirota equations with non-zero boundary conditions (NZBCs). The inverse problems are solved via the study of the matrix Riemann-Hilbert problems. As a consequence, we present the general solutions for the potentials, and explicit expressions for the reflectionless potentials. Moreover, the trace formulae and theta conditions are also given. Particularly, we discuss the simple-pole and double-pole solutions for the focusing case, and the simple-pole solutions for the defocusing case. Moreover, the results of the focusing case with NZBCs can reduce to ones of the focusing case with zero-boundary condition (ZBC). These obtained solutions are useful to explain the related nonlinear wave phenomena. (c) 2019Elsevier B.V. All rights reserved. |
| Keyword | Hirota equation Non-zero boundary conditions Inverse scattering Riemann-Hilbert problem Solitons Breathers |
| DOI | 10.1016/j.cnsns.2019.104927 |
| Language | 英语 |
| Funding Project | NSFC[11731014] ; NSFC[11571346] ; CAS Interdisciplinary Innovation Team |
| WOS Research Area | Mathematics ; Mechanics ; Physics |
| WOS Subject | Mathematics, Applied ; Mathematics, Interdisciplinary Applications ; Mechanics ; Physics, Fluids & Plasmas ; Physics, Mathematical |
| WOS ID | WOS:000490742900012 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35817 |
| Collection | 系统科学研究所 |
| Corresponding Author | Yan, Zhenya |
| Affiliation | 1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Zhang, Guoqiang,Chen, Shuyan,Yan, Zhenya. Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,2020,80:22. |
| APA | Zhang, Guoqiang,Chen, Shuyan,&Yan, Zhenya.(2020).Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions.COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,80,22. |
| MLA | Zhang, Guoqiang,et al."Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions".COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 80(2020):22. |
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