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On the Fractional Dynamics of Kinks in Sine-Gordon Models

Author

Listed:
  • Tassos Bountis

    (Department of Mathematics, University of Patras, 26500 Patras, Greece)

  • Julia Cantisán

    (Grupo de Física No Lineal (FQM-280), Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, 21071 Huelva, Spain)

  • Jesús Cuevas-Maraver

    (Grupo de Física No Lineal (FQM-280), Departamento de Física Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, C/ Virgen de África, 7, 41011 Sevilla, Spain
    Edificio Celestino Mutis, Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Avenida de la Reina Mercedes s/n, 41012 Sevilla, Spain)

  • Jorge Eduardo Macías-Díaz

    (Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia
    Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico)

  • Panayotis G. Kevrekidis

    (Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-4515, USA)

Abstract

In 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 β of the temporal derivative to that of a Caputo fractional type and found that, for 1 < β < 2 , this imposes a dissipative dynamical behavior on the coherent structures. We also examined the variation of a fractional Riesz order α on the spatial derivative. Here, depending on whether this order was below or above the harmonic value α = 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.

Suggested Citation

  • Tassos Bountis & Julia Cantisán & Jesús Cuevas-Maraver & Jorge Eduardo Macías-Díaz & Panayotis G. Kevrekidis, 2025. "On the Fractional Dynamics of Kinks in Sine-Gordon Models," Mathematics, MDPI, vol. 13(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:220-:d:1564449
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    References listed on IDEAS

    as
    1. Hao Ming & JinRong Wang & Michal Fečkan, 2019. "The Application of Fractional Calculus in Chinese Economic Growth Models," Mathematics, MDPI, vol. 7(8), pages 1-6, July.
    2. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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