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Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics
Zhang, Guoqiang1,2; Yan, Zhenya1,2; Wen, Xiao-Yong1,3
2018-03-01
Source PublicationPHYSICA D-NONLINEAR PHENOMENA
ISSN0167-2789
Volume366Pages:27-42
AbstractWe investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics. (C) 2017 Elsevier B.V. All rights reserved.
KeywordThree-wave resonant interactions Darboux transformation Multi-dark-dark-dark soliton Breathers Rogue waves Stability
DOI10.1016/j.physd.2017.11.001
Language英语
Funding ProjectNSFC[11731014] ; NSFC[11571346] ; Youth Innovation Promotion Association CAS
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000424174400003
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29614
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Beijing Informat Sci & Technol Univ, Sch Appl Sci, Dept Math, Beijing 100192, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Guoqiang,Yan, Zhenya,Wen, Xiao-Yong. Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics[J]. PHYSICA D-NONLINEAR PHENOMENA,2018,366:27-42.
APA Zhang, Guoqiang,Yan, Zhenya,&Wen, Xiao-Yong.(2018).Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics.PHYSICA D-NONLINEAR PHENOMENA,366,27-42.
MLA Zhang, Guoqiang,et al."Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics".PHYSICA D-NONLINEAR PHENOMENA 366(2018):27-42.
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