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Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation
Wen, Xiao-Yong1,2; Zhang, Guoqiang2,3
2018-01-10
Source PublicationMODERN PHYSICS LETTERS B
ISSN0217-9849
Volume32Issue:1Pages:21
AbstractUnder investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (m, N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1, N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.
KeywordGeneralized perturbation (n, N - n)-fold Darboux transformation the Kundu equation higher-order implicit RW solutions numerical simulations
DOI10.1142/S0217984918500057
Language英语
Funding ProjectChina Postdoctoral Science Foundation[2015M570161] ; Beijing Natural Science Foundation[1153004] ; NSFC[11375030] ; NSFC[11401031] ; Beijing Information Science and Technology University[QXTCP B201704] ; Qin Xin Talents Cultivation Program
WOS Research AreaPhysics
WOS SubjectPhysics, Applied ; Physics, Condensed Matter ; Physics, Mathematical
WOS IDWOS:000419927700013
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29304
Collection中国科学院数学与系统科学研究院
Affiliation1.Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China
2.Chinese Acad Sci, Key Lab Math Mech, Inst Syst Sci, AMSS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Wen, Xiao-Yong,Zhang, Guoqiang. Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation[J]. MODERN PHYSICS LETTERS B,2018,32(1):21.
APA Wen, Xiao-Yong,&Zhang, Guoqiang.(2018).Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation.MODERN PHYSICS LETTERS B,32(1),21.
MLA Wen, Xiao-Yong,et al."Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation".MODERN PHYSICS LETTERS B 32.1(2018):21.
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