KMS Of Academy of mathematics and systems sciences, CAS
| The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions | |
| Zhang, Guoqiang1; Yan, Zhenya2,3 | |
| 2020-07-17 | |
| Source Publication | JOURNAL OF NONLINEAR SCIENCE
 |
| ISSN | 0938-8974 |
| Pages | 39 |
| Abstract | In this paper, we report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary conditions (ZBCs) and nonzero boundary conditions (NZBCs) at infinity and double zeros of analytical scattering coefficients. The scattering theories for both ZBCs and NZBCs are addressed. The direct scattering problem establishes the analyticity, symmetries, and asymptotic behaviors of the Jost solutions and scattering matrix, and properties of discrete spectra. The inverse scattering problems are formulated and solved with the aid of the matrix Riemann-Hilbert problems, and the reconstruction formulae, trace formulae and theta conditions are also posed. In particular, the IST with NZBCs at infinity is proposed by a suitable uniformization variable, which allows the scattering problem to be solved on a standard complex plane instead of a two-sheeted Riemann surface. The reflectionless potentials with double poles for the ZBCs and NZBCs are both carried out explicitly by means of determinants. Some representative semi-rational bright-bright soliton, dark-bright soliton, and breather-breather solutions are examined in detail. These results and idea can also be extended to other types of DNLS equations such as the Chen-Lee-Liu-type DNLS equation, Gerdjikov-Ivanov-type DNLS equation, and Kundu-type DNLS equation and will be useful to further explore and apply the related nonlinear wave phenomena. |
| Keyword | Derivative nonlinear Schrodinger equation Modified Zakharov-Shabat eigenvalue problem Inverse scattering Riemann-Hilbert problem Zero nonzero boundary conditions Double-pole solitons and breathers |
| DOI | 10.1007/s00332-020-09645-6 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSFC[11925108] ; NSFC[11731014] ; CAS Interdisciplinary Innovation Team |
| WOS Research Area | Mathematics ; Mechanics ; Physics |
| WOS Subject | Mathematics, Applied ; Mechanics ; Physics, Mathematical |
| WOS ID | WOS:000549683700001 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51823 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yan, Zhenya |
| Affiliation | 1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Key Lab Math Mechanizat, Acad Math & Syst Sci, 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,Yan, Zhenya. The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions[J]. JOURNAL OF NONLINEAR SCIENCE,2020:39. |
| APA | Zhang, Guoqiang,&Yan, Zhenya.(2020).The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions.JOURNAL OF NONLINEAR SCIENCE,39. |
| MLA | Zhang, Guoqiang,et al."The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions".JOURNAL OF NONLINEAR SCIENCE (2020):39. |
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