Xu, S., Wang, L., Erdélyi, R. et al. (1 more author) (2019) Degeneracy in bright–dark solitons of the Derivative Nonlinear Schrödinger equation. Applied Mathematics Letters, 87. pp. 64-72. ISSN 0893-9659
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 λk→λc1(λc2), where λc1(λc2) 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier. |
Keywords: | Derivative Nonlinear Schrödinger equation; Bright–dark solitons degeneration; Quasi-rational solutions; Rogue waves; Darboux transformation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Oct 2018 11:56 |
Last Modified: | 15 Oct 2018 11:56 |
Published Version: | https://doi.org/10.1016/j.aml.2018.07.021 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.aml.2018.07.021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:137157 |