@article{10272/24849,
year = {2025},
month = {1},
url = {https://hdl.handle.net/10272/24849},
abstract = {In the present work we explore 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 modify the order β  of the temporal derivative to that of a Caputo fractional type and find that, for 1 < β < 2, this imposes a dissipative dynamical behavior on the coherent structures. We also examine the variation of a fractional Riesz order α on the spatial derivative. Here, depending on whether this order is below or above the harmonic value α = 2, we find, respectively, monotonically attracting kinks, or non-monotonic and potentially attracting or repelling kinks, with a saddle equilibrium separating the two. Finally, we also explore the interplay of the two derivatives, when both Caputo temporal and Riesz spatial derivatives are involved.},
organization = {J.E.M.-D.: The present work reports on a set of final results of the research project “Conservative
methods for fractional hyperbolic systems: analysis and applications”, which was funded by
the National Council for Science and Technology of Mexico (CONACYT) through grant A1-S-45928.
This material is based upon work supported by the U.S. National Science Foundation under the
awards PHY-2110030, PHY-2408988 and DMS-2204702 (PGK). J.C.-M. acknowledges support from
the EU (FEDER program 2014–2020) through MCIN/AEI/10.13039/501100011033 (under the projects
PID2020-112620GB-I00 and PID2022-143120OB-I00). J.C. acknowledges that this work has been
supported by the Spanish State Research Agency (AEI) and the European Regional Development
Fund (ERDF, EU) under project PID2023-148160NB-I00 (MCIN/AEI/10.13039/501100011033).},
publisher = {MDPI},
title = {On the Fractional Dynamics of Kinks in Sine-Gordon Models},
doi = {10.3390/math13020220},
author = {Bountis, Tassos and Cantisán Gómez, Julia and Cuevas Maraver, Jesús and Macías Díaz, Jorge Eduardo and Kevrekidis, Panayotis G.},
}