Dynamics of higher-order localized waves for a coupled nonlinear Schrödinger equation

• Published in: Communications in nonlinear science & numerical simulation 2020-03, Vol.82, p.105046, Article 105046
• Main Authors: Song, N., Xue, H., Xue, Y.K.
• Format: Article
• Language: English
• Subjects: Breathers; Coupled nonlinear Schrödinger equation; Generalized Darboux transformation; Localized waves; Nonlinear equations; Schrodinger equation; Solitary waves; Surface waves
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.105046

•Higher-order localized wave solutions are studied for a coupled nonlinear Schrödinger equation.•A new form of seed solutions is supposed.•Dynamics of localized waves are discussed, especially the third-order ones, which are not studied in the previous paper.•Display some interesting and novel plots. In this paper, dynamics of higher-order localized waves for a coupled nonlinear Schrödinger equation are investigated. Based on the generalized Darboux transformation, the first- to the third-order interactional localized wave solutions are derived through algebraic iteration. Specially, the new form of seed solutions is supposed, which is related to the normalized distance and retarded time. Many novel dynamic structures are demonstrated in the localized waves, particularly the third-order localized ones, where rogue waves coexist with dark-bright solitons and breathers in the three-dimensional plots. Furthermore, the classification of the Nth-order localized waves is given in the form of a table. In addition, an interesting phenomenon is observed that the order of rogue waves and the number of dark-bright solitons and breathers are consistent with the order of localized waves. These appealing results will be helpful to enrich the studies of localized waves for the coupled system.