Fractal structure of the soliton scattering for the graphene superlattice equation

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 kink...

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Bibliographic Details
Published inChaos, solitons and fractals Vol. 151; p. 111281
Main Authors Martin-Vergara, Francisca, Rus, Francisco, Villatoro, Francisco R.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.10.2021
Subjects
Computational simulations
Fractal structure
Graphene superlattice equation
Kink-antikink scattering
Fractal structure
Graphene superlattice equation
Kink-antikink scattering
Computational simulations
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Summary: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.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2021.111281