Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
文献类型：期刊论文
| 作者 | Zhang, Guoqiang1; Yan, Zhenya2,3 |
| 刊名 | PHYSICA D-NONLINEAR PHENOMENA
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000512219900001 |
| 出版者 | ELSEVIER |
| 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.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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。