On the fractional dynamics of kinks in sine-Gordon models
I the present work, we explored the dynamics of single kinks, kink–anti-kink pairs and bound states in the prototypical fractional Klein–Gordon example of the sine-Gordon equation. In particular, we modified the order of the temporal derivative to that of a Caputo fractional type and found that, for...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/168812 |
| Acceso en línea: | https://hdl.handle.net/11441/168812 https://doi.org/10.3390/math13020220 |
| Access Level: | acceso abierto |
| Palabra clave: | sine-Gordon equation Kinks Breathers Fractional derivatives Caputo derivative Riesz derivative |
| Sumario: | I the present work, we explored the dynamics of single kinks, kink–anti-kink pairs and bound states in the prototypical fractional Klein–Gordon example of the sine-Gordon equation. In particular, we modified the order of the temporal derivative to that of a Caputo fractional type and found that, for 1<<2, this imposes a dissipative dynamical behavior on the coherent structures. We also examined the variation of a fractional Riesz order on the spatial derivative. Here, depending on whether this order was below or above the harmonic value =2, we found, respectively, monotonically attracting kinks, or non-monotonic and potentially attracting or repelling kinks, with a saddle equilibrium separating the two. Finally, we also explored the interplay of the two derivatives, when both Caputo temporal and Riesz spatial derivatives are involved. |
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