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.The authors thank the reviewers for their thoughtful comments and efforts toward improving our manuscript. The research reported here was supported by Project RoCoSoyCo (UMA18-FEDERJA-248) of the Consejería de Economía y Conocimiento, Junta de Andalucía, Spain.
Funding for open access charge: Universidad de Málaga / CBU
