Degeneracy in bright-dark solitons of the Derivative Nonlinear Schrödinger equation

Abstract Bright–dark soliton interactions modelled by the Derivative Nonlinear Schrodinger (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.

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