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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| Published in | Chaos, solitons and fractals Vol. 151; p. 111281 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.10.2021
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 111281 |
| Author | Rus, Francisco Villatoro, Francisco R. Martin-Vergara, Francisca |
| Author_xml | – sequence: 1 givenname: Francisca orcidid: 0000-0003-1478-8444 surname: Martin-Vergara fullname: Martin-Vergara, Francisca email: fmarver@uma.es – sequence: 2 givenname: Francisco orcidid: 0000-0002-7641-0255 surname: Rus fullname: Rus, Francisco email: fdrus@uma.es – sequence: 3 givenname: Francisco R. orcidid: 0000-0003-4314-6213 surname: Villatoro fullname: Villatoro, Francisco R. email: frvillatoro@uma.es |
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| Keywords | Fractal structure Graphene superlattice equation Kink-antikink scattering Computational simulations |
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