Bountis, TassosCantisán Gómez, JuliaCuevas Maraver, JesúsMacías Díaz, Jorge EduardoKevrekidis, Panayotis G.2025-01-202025-01-202025-01Bountis, 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/math130202202227-7390 (electrónico)https://hdl.handle.net/10272/24849In 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.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Sine-Gordon equationKinks; breathersFractional derivativesCaputo derivativeRiesz derivativejournal article10.3390/math13020220open access22 Física