Solutions of the lattice sine-Gordon equation and the solitons of its cellular automaton
Solutions of the lattice sine-Gordon equation and the solitons of its cellular automaton
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格子正弦-戈登方程及其元胞自动机孤子的解
DOI：
10.1088/1751-8113/47/12/125202
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Ramani and B. Grammaticos
中科院分区：
文献类型：
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作者：
R. Willox;A. Ramani and B. Grammaticos
我们分析了元胞自动机Sine-Gordon方程的解，并将它们与离散的、格子的、Sine-Gordon方程的解联系起来。我们证明了，尽管后者的超离散、正定解表现为弥散行为，但这些色散波的某些部分仍然在超离散极限中存活，从而产生了元胞自动机的解。我们研究了广义元胞自动机情况下的超离散解，其中因变量可以取非整数值，我们证明了两个孤立波的碰撞是非弹性的，导致了连接两个传出结构的固定高度的“桥”的产生。基于Sine-Gordon方程的超离散形式，我们解释了这一桥接区的出现，并描述了它与孤立波的相互作用。
We analyse the solutions of the cellular automaton sine–Gordon equation and link them to solutions of the discrete, lattice, sine–Gordon. We show that while the ultradiscretizable, positive definite, solutions of the latter behave dispersively, certain parts of these dispersive waves nonetheless survive in the ultradiscrete limit, giving rise to the solutions of the cellular automaton. We examine the ultradiscrete solutions in the case of a generalized cellular automaton in which the dependent variable can assume non-integer values and we show that the collision of two solitary waves is inelastic, leading to the creation of a'bridge'of constant height that links two outgoing structures. Based on the ultradiscrete form of the sine–Gordon equation we explain the appearance of this bridging region and we describe its interaction with a solitary wave.