Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions

doi:10.1016/j.physd.2019.132170

	Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
	Zhang, Guoqiang 2; Yan, Zhenya 1,3
刊名	PHYSICA D-NONLINEAR PHENOMENA
	2020-01-15
卷号	402 页码:14
关键词	Nonlocal mKdV equation Non-zero boundary conditions Riemann surface Inverse scattering transform Matrix Riemann-Hilbert problem Solitons
ISSN号	0167-2789
DOI	10.1016/j.physd.2019.132170
英文摘要	In this paper, we present a systematical inverse scattering transform for both focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity. The suitable uniformization variable is introduced to make the direct and inverse scattering problems be established on a new complex plane instead of the two-sheeted Riemann surface. The direct scattering problem establishes the analyticity, symmetries and asymptotic behaviors of Jost solutions and scattering matrix, and properties of discrete spectrum. The inverse scattering problem is solved by means of a corresponding matrix-valued Riemann-Hilbert problem. The reconstruction formula for the potential, trace formulae, and theta conditions are found. Finally, the dynamical behaviors of solitons and their interactions for four distinct cases of the reflectionless potentials for both focusing and defocusing nonlocal mKdV equations with NZBCs are analyzed in detail. (C) 2019 Elsevier B.V. All rights reserved.
资助项目	NSFC, China[11731014] ; NSFC, China[61621003] ; NSFC, China[11925108] ; CAS, China Interdisciplinary Innovation Team
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000512219900001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50792]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Guoqiang,Yan, Zhenya. Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions[J]. PHYSICA D-NONLINEAR PHENOMENA,2020,402:14.
APA	Zhang, Guoqiang,&Yan, Zhenya.(2020).Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions.PHYSICA D-NONLINEAR PHENOMENA,402,14.
MLA	Zhang, Guoqiang,et al."Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions".PHYSICA D-NONLINEAR PHENOMENA 402(2020):14.