Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation

doi:10.1063/1.4937925

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	Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation
	Wen, Xiao-Yong 1,2; Yan, Zhenya1
	2015-12-01
发表期刊	CHAOS
ISSN	1054-1500
卷号	25 期号:12 页码:13
摘要	We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields. (C) 2015 AIP Publishing LLC.
DOI	10.1063/1.4937925
语种	英语
资助项目	Beijing Natural Science Foundation[1153004] ; China Postdoctoral Science Foundation[2015M570161] ; NSFC[11375030] ; NSFC[61178091]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000367534200015
出版者	AMER INST PHYSICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21644
专题	系统科学研究所
通讯作者	Wen, Xiao-Yong
作者单位	1.Chinese Acad Sci, AMSS, Inst Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Beijing Informat Sci & Technol Univ, Sch Appl Sci, Dept Math, Beijing 100192, Peoples R China
推荐引用方式 GB/T 7714	Wen, Xiao-Yong,Yan, Zhenya. Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation[J]. CHAOS,2015,25(12):13.
APA	Wen, Xiao-Yong,&Yan, Zhenya.(2015).Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.CHAOS,25(12),13.
MLA	Wen, Xiao-Yong,et al."Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation".CHAOS 25.12(2015):13.