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Numerical search for the stationary quasi-breather of the graphene superlattice equation

Author

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

Abstract

The propagation of electromagnetic solitons in a graphene superlattice device is governed by a modified sine-Gordon equation, referred to as the graphene superlattice equation. Kink-antikink collisions suggest the existence of a quasi-breather solution. Here, a numerical search for static quasi-breathers is undertaken by using a new initial condition obtained by a regular perturbation of the null solution. Our results show that the frequency of the initial condition has a minimum critical value for the appearance of a robust quasi-breather able to survive during more than one thousand periods. The amplitude and energy of the quasi-breather solution decrease, but its frequency increases, as time grows. The robustness of the new quasi-breather supports its experimental search in real graphene superlattice devices.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007287
    DOI: 10.1016/j.chaos.2022.112530
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    1. 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).
    2. 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).

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    3. Mohammadi, M. & Momeni, E., 2022. "Scattering of kinks in the Bφ4 model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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