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Fractal structure of the soliton scattering for the graphene superlattice equation

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  • Martin-Vergara, Francisca
  • Rus, Francisco
  • Villatoro, Francisco R.

Abstract

The graphene superlattice equation, a modified sine-Gordon equation, governs the propagation of solitary electromagnetic waves in a graphene superlattice. This equation has kink solutions without explicit analytical expression, requiring the use of quadrature methods. The inelastic collision of kinks and antikinks with the same but opposite speed is studied numerically for the first time; after their interaction they escape to infinity when its speed is either larger than a critical value or it is inside a series of resonance windows; otherwise, they form a breather-like state that slowly decays by radiating energy. Here, the fractal structure of these resonance windows is characterized by using a multi-index notation and their main features are compared with the predictions of the resonant energy exchange theory showing good agreement. Our results can be interpreted as new evidence in favour of this theory.

Suggested Citation

  • Martin-Vergara, Francisca & Rus, Francisco & Villatoro, Francisco R., 2021. "Fractal structure of the soliton scattering for the graphene superlattice equation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006354
    DOI: 10.1016/j.chaos.2021.111281
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    References listed on IDEAS

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    1. El-Ganaini, Shoukry & Kumar, Hitender, 2020. "A variety of new traveling and localized solitary wave solutions of a nonlinear model describing the nonlinear low- pass electrical transmission lines," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Askari, Alidad & Moradi Marjaneh, Aliakbar & Rakhmatullina, Zhanna G. & Ebrahimi-Loushab, Mahdy & Saadatmand, Danial & Gani, Vakhid A. & Kevrekidis, Panayotis G. & Dmitriev, Sergey V., 2020. "Collision of ϕ4 kinks free of the Peierls–Nabarro barrier in the regime of strong discreteness," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Martin-Vergara, Francisca & Rus, Francisco & Villatoro, Francisco R., 2019. "Padé numerical schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 232-243.
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    Cited by:

    1. Mohammadi, M. & Momeni, E., 2022. "Scattering of kinks in the Bφ4 model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Martin-Vergara, Francisca & Rus, Francisco & Villatoro, Francisco R., 2022. "Numerical search for the stationary quasi-breather of the graphene superlattice equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Moradi Marjaneh, Aliakbar & Simas, Fabiano C. & Bazeia, D., 2022. "Collisions of kinks in deformed φ4 and φ6 models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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