KP Solitons, Higher Bruhat and Tamari Orders

  title={KP Solitons, Higher Bruhat and Tamari Orders},
  author={Aristophanes Dimakis and Folkert Mueller-Hoissen},
  journal={arXiv: Combinatorics},
In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planar rooted binary trees, connected by right rotation. More precisely, it determines a maximal chain of a Tamari lattice. We show that an analysis of these solutions naturally involves higher Bruhat and higher Tamari orders. 
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