Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions

doi:10.1016/j.physd.2020.132521

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	Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions
	Zhang, Guoqiang 1; Yan, Zhenya 2,3
	2020-09-01
发表期刊	PHYSICA D-NONLINEAR PHENOMENA
ISSN	0167-2789
卷号	410 页码:22
摘要	We explore the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity systematically. Using a suitable uniformization variable, the direct and inverse scattering problems are proposed on a complex plane instead of a two-sheeted Riemann surface. For the direct scattering problem, the analyticities, symmetries and asymptotic behaviors of the Jost solutions and scattering matrix, and discrete spectra are established. The inverse problems are formulated and solved with the aid of the matrix Riemann-Hilbert problems, and the reconstruction formulas, trace formulas, and theta conditions are also posed. In particular, we present the general solutions for the focusing mKdV equation with NZBCs and both simple and double poles, and for the defocusing mKdV equation with NZBCs and simple poles. Finally, some representative reflectionless potentials are in detail studied to illustrate distinct nonlinear wave structures containing solitons and breathers for both focusing and defocusing mKdV equations with NZBCs. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Focusing and defocusing mKdV equations Non-zero boundary conditions Direct and inverse scattering Riemann-Hilbert problem Multi-soliton solutions Breathers
DOI	10.1016/j.physd.2020.132521
收录类别	SCI
语种	英语
资助项目	NSFC, China[11925108] ; NSFC, China[11731014] ; CAS, China Interdisciplinary Innovation Team
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Fluids & Plasmas ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000538603700008
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/51612
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, 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,Yan, Zhenya. Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions[J]. PHYSICA D-NONLINEAR PHENOMENA,2020,410:22.
APA	Zhang, Guoqiang,&Yan, Zhenya.(2020).Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions.PHYSICA D-NONLINEAR PHENOMENA,410,22.
MLA	Zhang, Guoqiang,et al."Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions".PHYSICA D-NONLINEAR PHENOMENA 410(2020):22.