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.

石墨烯超晶格器件中电磁孤子的传播受修正的正弦-戈登方程控制，称为石墨烯超晶格方程。扭结-反扭结碰撞表明存在准呼吸解决方案。在这里，通过使用由零解的规则扰动获得的新初始条件来进行静态准呼吸器的数值搜索。我们的结果表明，初始条件的频率对于能够在一千多个周期内存活的稳健准呼吸器的出现具有最小临界值。随着时间的增长，准呼吸溶液的幅度和能量会降低，但其频率会增加。新准呼吸器的稳健性支持其在真实石墨烯超晶格器件中的实验搜索。