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

• Published in: Chaos, solitons and fractals Vol. 162; p. 112530
• Main Authors: Martin-Vergara, Francisca, Rus, Francisco, Villatoro, Francisco R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2022
• Subjects: Computational simulations; Finite difference method; Modified sine-Gordon equation; Nonlinear electromagnetic waves; Solitons; Nonlinear electromagnetic waves; Computational simulations; Modified sine-Gordon equation; Solitons; Finite difference method
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112530

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. •Numerical search for static quasi-breathers using a new initial condition obtained by a regular perturbation of the null solution.•Appearance of a robust quasi-breather after a minimum critical value for the frequency of the initial condition.•The robustness of the new quasi-breather supports its experimental search in real graphene superlattice devices.