石墨烯超晶格方程孤子散射的分形结构
Fractal structure of the soliton scattering for the graphene superlattice equation
摘要：
石墨烯超晶格方程是一个修正的sine-Gordon方程，它控制着孤立电磁波在石墨烯超晶格中的传播。该方程有扭结解，没有显式的解析表达式，需要使用求积方法。本文首次对扭结和反扭结的非弹性碰撞进行了数值研究，当它们相互作用后，当它们的速度大于临界值或处于一系列共振窗口内时，它们逃逸到无穷远;否则，它们形成一个类似呼吸器的状态，通过辐射能量缓慢衰减。在这里，这些共振窗口的分形结构的特点是通过使用多指数符号和它们的主要特点进行比较的共振能量交换理论的预测，表现出良好的一致性。我们的结果可以解释为支持这一理论的新证据。
英文摘要：
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.
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