KMS Of Academy of mathematics and systems sciences, CAS
| Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions | |
| Zhang, Guoqiang1; Yan, Zhenya2,3 | |
| 2020-01-15 | |
| Source Publication | PHYSICA D-NONLINEAR PHENOMENA
 |
| ISSN | 0167-2789 |
| Volume | 402Pages:14 |
| Abstract | 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. |
| Keyword | Nonlocal mKdV equation Non-zero boundary conditions Riemann surface Inverse scattering transform Matrix Riemann-Hilbert problem Solitons |
| DOI | 10.1016/j.physd.2019.132170 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSFC, China[11731014] ; NSFC, China[61621003] ; NSFC, China[11925108] ; CAS, China Interdisciplinary Innovation Team |
| WOS Research Area | Mathematics ; Physics |
| WOS Subject | Mathematics, Applied ; Physics, Fluids & Plasmas ; Physics, Multidisciplinary ; Physics, Mathematical |
| WOS ID | WOS:000512219900001 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50793 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yan, Zhenya |
| Affiliation | 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 |
| Recommended Citation 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. |
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