Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions

doi:10.1016/j.physleta.2021.127472

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	Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions
	Weng, Weifang 1,2; Yan, Zhenya 1,2
	2021-08-16
发表期刊	PHYSICS LETTERS A
ISSN	0375-9601
卷号	407 页码:18
摘要	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.
关键词	Focusing NLS hierarchy Inverse scattering Riemann-Hilbert problem Nonzero boundary conditions N-triple-pole solitons and breathers
DOI	10.1016/j.physleta.2021.127472
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11731014] ; National Natural Science Foundation of China[11925108]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000658347200001
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58750
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.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
推荐引用方式 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.