Numerical search for the stationary quasi-breather of the graphene superlattice equation. - Martín-Vergara, Francisca; Rus-Mansilla, Francisco de Asís; Villatoro-Machuca, Francisco Román (ELSEVIER, 2022)
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.
Keywords: Grafeno; Ondas electromagnéticas; Superredes; Nonlinear electromagnetic waves; Solitons; Computational simulations; Modified sine-Gordon equation; Finite difference method