Degeneracy in bright–dark solitons of the Derivative Nonlinear Schrödinger equation. (January 2019)

• Record Type: Journal Article
• Authors: Xu, Shuwei; Wang, Lihong; Erdélyi, R.; He, Jingsong
• Is Part Of: Applied mathematics letters. Volume 87(2019)
• Page Start: 64
• Page End: 72
• Publication Date: 2019-01
• Subjects: Derivative Nonlinear Schrödinger equation -- Bright–dark solitons degeneration -- Quasi-rational solutions -- Rogue waves -- Darboux transformation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.07.021
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Bright–dark soliton interactions modelled by the Derivative Nonlinear Schrödinger (DNLS) equation are constructed from non-vanishing boundary conditions by the N-fold Darboux transformation. Adjusting the limitation λ k → λ c 1 ( λ c 2 ), where λ c 1 ( λ c 2 ) is a critical eigenvalue associated with the synchronization of the relative phase of the bright–dark solitons in the interacting area, enables to obtain different types of quasi-rational solutions from the bright–dark solitons degeneration. Namely, quasi-rational bright and dark solitons, quasi-rational bright–dark solitons and rogue waves are found. Since a large number of preceding researchers have already addressed the relationship between the breather solutions and rogue waves, a more general modelling of rogue waves can be realized via the consideration of degeneration of bright–dark solitons. Hence, the phenomenon discussed here represents a novel nonlinear mechanism for the generation of rogue waves.