Fractional discrete vortex solitons
We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional ex...
- Autores:
-
Mejía-Cortés, Cristian
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad del Atlántico
- Repositorio:
- Repositorio Uniatlantico
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniatlantico.edu.co:20.500.12834/1137
- Acceso en línea:
- https://hdl.handle.net/20.500.12834/1137
- Palabra clave:
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
| Summary: | We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent α, becoming effectively long-range at small α values. At long-distance, it can be shown that this coupling decreases faster than exponential: ∼ exp(−|n|)/ p |n|. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower power levels, as the α coefficient diminishes, independently of their topological charge and/or pattern distribution. |
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