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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 PublicationJOURNAL OF NONLINEAR SCIENCE
ISSN0938-8974
Pages39
AbstractIn 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.
KeywordDerivative nonlinear Schrodinger equation Modified Zakharov-Shabat eigenvalue problem Inverse scattering Riemann-Hilbert problem Zero nonzero boundary conditions Double-pole solitons and breathers
DOI10.1007/s00332-020-09645-6
Indexed BySCI
Language英语
Funding ProjectNSFC[11925108] ; NSFC[11731014] ; CAS Interdisciplinary Innovation Team
WOS Research AreaMathematics ; Mechanics ; Physics
WOS SubjectMathematics, Applied ; Mechanics ; Physics, Mathematical
WOS IDWOS:000549683700001
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51823
Collection中国科学院数学与系统科学研究院
Corresponding AuthorYan, Zhenya
Affiliation1.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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