RT Journal Article
T1 On the Fractional Dynamics of Kinks in Sine-Gordon Models
A1 Bountis, Tassos
A1 Cantisán Gómez, Julia
A1 Cuevas Maraver, Jesús
A1 Macías Díaz, Jorge Eduardo
A1 Kevrekidis, Panayotis G.
AB 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.
PB MDPI
SN 2227-7390 (electrónico)
YR 2025
FD 2025-01
LK https://hdl.handle.net/10272/24849
UL https://hdl.handle.net/10272/24849
LA eng
NO Bountis, T., Cantisán, J., Cuevas-Maraver, J., Macías-Díaz, J. E., & Kevrekidis, P. G. (2025). On the Fractional Dynamics of Kinks in Sine-Gordon Models. In Mathematics (Vol. 13, Issue 2, p. 220). MDPI AG. https://doi.org/10.3390/math13020220
NO J.E.M.-D.: The present work reports on a set of final results of the research project “Conservativemethods for fractional hyperbolic systems: analysis and applications”, which was funded bythe 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 theawards PHY-2110030, PHY-2408988 and DMS-2204702 (PGK). J.C.-M. acknowledges support fromthe EU (FEDER program 2014–2020) through MCIN/AEI/10.13039/501100011033 (under the projectsPID2020-112620GB-I00 and PID2022-143120OB-I00). J.C. acknowledges that this work has beensupported by the Spanish State Research Agency (AEI) and the European Regional DevelopmentFund (ERDF, EU) under project PID2023-148160NB-I00 (MCIN/AEI/10.13039/501100011033).
DS Repositorio Institucional de la Universidad de Huelva
RD 30 may 2026