Existence, stability and spatio-temporal dynamics of time-quasiperiodic solutions on a finite background in discrete nonlinear Schrödinger models
In the present work we explore the potential of models of the discrete nonlinear Schrödinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously shown to exist in the vicinity of the anti-continuum, vanishing-...
| Autores: | , , , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/158073 |
| Acesso em linha: | https://hdl.handle.net/11441/158073 https://doi.org/10.1016/j.wavemoti.2024.103324 |
| Access Level: | acceso abierto |
| Palavra-chave: | Discrete nonlinear Schrödinger equation Solitons Breathers Discrete solitons Quasi-periodic solitons Rogue waves |
| Resumo: | In the present work we explore the potential of models of the discrete nonlinear Schrödinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously shown to exist in the vicinity of the anti-continuum, vanishing-coupling limit of the model. We then use numerical continuation to illustrate their persistence for finite coupling, as well as to explore their spectral stability. We obtain an intricate bifurcation diagram showing a progression of such solutions from simpler ones bearing single- and two-site excitations to more complex, multi-site ones with a direct connection of the branches of the self-focusing and self-defocusing nonlinear regime. We further probe the variation of the solutions obtained towards the limit of vanishing frequency for both signs of the nonlinearity. Our analysis is complemented by exploring the dynamics of the solutions via direct numerical simulations. |
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