Fractal structure of the soliton scattering for the graphene superlattice equation

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.

27 pages, 10 figures, 3 tables

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Cited by in corpus (10)

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• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Fermionic spectral walls in kink collisions
• Sphalerons and resonance phenomenon in kink-antikink collisions
• Noise-induced, ac-stabilized sine-Gordon breathers: Emergence and statistics
• Scattering of kinks in the $B{\phi }^4$ model
• Collective coordinates for the hybrid model
• Dynamics of localized solutions in three core coupled waveguides with quasi-periodic nonlinearity
• Breather solution of non-linear Klein-Gordon equation