Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions

doi:10.1016/j.cnsns.2019.104927

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	Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions
	Zhang, Guoqiang 1; Chen, Shuyan 2,3; Yan, Zhenya2,3
刊名	COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
	2020
卷号	80 页码:22
关键词	Hirota equation Non-zero boundary conditions Inverse scattering Riemann-Hilbert problem Solitons Breathers
ISSN号	1007-5704
DOI	10.1016/j.cnsns.2019.104927
英文摘要	In this paper, we investigate the inverse scattering transforms and soliton solutions of both focusing and defocusing Hirota equations with non-zero boundary conditions (NZBCs). The inverse problems are solved via the study of the matrix Riemann-Hilbert problems. As a consequence, we present the general solutions for the potentials, and explicit expressions for the reflectionless potentials. Moreover, the trace formulae and theta conditions are also given. Particularly, we discuss the simple-pole and double-pole solutions for the focusing case, and the simple-pole solutions for the defocusing case. Moreover, the results of the focusing case with NZBCs can reduce to ones of the focusing case with zero-boundary condition (ZBC). These obtained solutions are useful to explain the related nonlinear wave phenomena. (c) 2019Elsevier B.V. All rights reserved.
资助项目	NSFC[11731014] ; NSFC[11571346] ; CAS Interdisciplinary Innovation Team
WOS研究方向	Mathematics ; Mechanics ; Physics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000490742900012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35816]
专题	系统科学研究所
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, Acad Math & Syst Sci, Key Lab Math Mechanizat, 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,Chen, Shuyan,Yan, Zhenya. Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,2020,80:22.
APA	Zhang, Guoqiang,Chen, Shuyan,&Yan, Zhenya.(2020).Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions.COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,80,22.
MLA	Zhang, Guoqiang,et al."Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions".COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 80(2020):22.