The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions

doi:10.1007/s00332-020-09645-6

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	The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions
	Zhang, Guoqiang 1; Yan, Zhenya 2,3
	2020-07-17
发表期刊	JOURNAL OF NONLINEAR SCIENCE
ISSN	0938-8974
页码	39
摘要	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.
关键词	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
收录类别	SCI
语种	英语
资助项目	NSFC[11925108] ; NSFC[11731014] ; CAS Interdisciplinary Innovation Team
WOS研究方向	Mathematics ; Mechanics ; Physics
WOS类目	Mathematics, Applied ; Mechanics ; Physics, Mathematical
WOS记录号	WOS:000549683700001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51823
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.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
推荐引用方式 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.