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

CSpace

	Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
	Zhang, Guoqiang 1; Yan, Zhenya 2,3
	2020-01-15
发表期刊	PHYSICA D-NONLINEAR PHENOMENA
ISSN	0167-2789
卷号	402 页码:14
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.
关键词	Nonlocal mKdV equation Non-zero boundary conditions Riemann surface Inverse scattering transform Matrix Riemann-Hilbert problem Solitons
DOI	10.1016/j.physd.2019.132170
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Physics, Fluids & Plasmas ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000512219900001
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/50793
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. 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.