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arXiv · 2411.18600

On the Fractional Dynamics of Kinks in sine-Gordon Models

T. Bountis·J. Cantisán·J. Cuevas-Maraver·J. E. Macías-Díaz·P. G. Kevrekidis
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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 $\beta$ of the temporal derivative to that of a Caputo fractional type and find that, for $1<\beta<2$, this imposes a dissipative dynamical behavior on the coherent structures. We also examine the variation of a fractional Riesz order $\alpha$ on the spatial derivative. Here, depending on whether this order is below or above the harmonic value $\alpha=2$, 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.

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T. Bountis, J. Cantisán, J. Cuevas-Maraver, J. E. Macías-Díaz, P. G. Kevrekidis. 2024-11-27. On the Fractional Dynamics of Kinks in sine-Gordon Models. https://doi.org/10.3390/math13020220

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