KMS Of Academy of mathematics and systems sciences, CAS
Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions | |
Weng, Weifang1,2; Yan, Zhenya1,2 | |
2021-08-16 | |
Source Publication | PHYSICS LETTERS A |
ISSN | 0375-9601 |
Volume | 407Pages:18 |
Abstract | Based on the matrix Riemann-Hilbert problem we present the inverse scattering transform for the focusing nonlinear Schrodinger (NLS) equation with nonzero boundary conditions (NZBCs) at infinity and triple zerosof analytical scattering coefficients. As a consequence, the inverse scattering problem can be solved via the study of the matrix Riemann-Hilbert problem with triple poles. We find the general Ntriple-pole solutions for the potential, and explicit N-triple-pole expression for the reflectionless potential in terms of two determinants. Besides, the trace formulae and theta conditions are also given. Finally, we discuss the one-triple-pole breather-breather-breather solution for the focusing NLS equation with NZBCs. Moreover, the general N-triple-pole breathers of NZBCs can reduce to general N-triple-pole solitons of the zero-boundary conditions. These results can also be extended to the focusing higher-order NLS equations (i.e., the NLS hierarchy such as the Hirota equation, complex mKdV equation, Lakshmanan-Porsezian-Daniel equation, complex fifth-order mKdV equation, fifth-, sixth-, and seventh-order NLS equations, etc.) with NZBCs to find their inverse scattering transforms (ISTs) and N-triple-pole solutions. These obtained triple-pole solutions are useful to explain the related nonlinear wave phenomena. (C) 2021 Elsevier B.V. All rights reserved. |
Keyword | Focusing NLS hierarchy Inverse scattering Riemann-Hilbert problem Nonzero boundary conditions N-triple-pole solitons and breathers |
DOI | 10.1016/j.physleta.2021.127472 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11731014] ; National Natural Science Foundation of China[11925108] |
WOS Research Area | Physics |
WOS Subject | Physics, Multidisciplinary |
WOS ID | WOS:000658347200001 |
Publisher | ELSEVIER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58750 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Yan, Zhenya |
Affiliation | 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 |
Recommended Citation GB/T 7714 | Weng, Weifang,Yan, Zhenya. Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions[J]. PHYSICS LETTERS A,2021,407:18. |
APA | Weng, Weifang,&Yan, Zhenya.(2021).Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions.PHYSICS LETTERS A,407,18. |
MLA | Weng, Weifang,et al."Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions".PHYSICS LETTERS A 407(2021):18. |
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