KP line solitons and Tamari lattices
KP line solitons and Tamari lattices
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KP 线孤子和 Tamari 格子
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
F. Mueller
中科院分区：
文献类型：
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作者：
A. Dimakis;F. Mueller
Kadomtsev Petviashvili（KP）II方程具有一类线孤子的解决方案，可以定性地描述通过热带近似作为一个链的根二叉树，除了在“关键”的事件发生的过渡到一个不同的根二叉树。我们证明，这些对应于最大链的Tamari格（这是偏序集结构上的associahedra）。我们进一步得出的结果，使我们能够计算的演变，包括关键事件的细节。此外，我们提出了更一般的线孤子解的结构的一些见解。所有这一切都产生了表征浅流体表面上的线孤子模式的可能演变（提供的KP-II近似适用）。
The Kadomtsev–Petviashvili (KP) II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at ‘critical’ events where a transition to a different rooted binary tree takes place. We prove that these correspond to maximal chains in Tamari lattices (which are poset structures on associahedra). We further derive results that allow us to compute details of the evolution, including the critical events. Moreover, we present some insights into the structure of the more general line soliton solutions. All this yields a characterization of possible evolutions of line soliton patterns on a shallow fluid surface (provided that the KP-II approximation applies).