KP solitons, higher Bruhat and Tamari orders
  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. 
Aristophanes Dimakis and Folkert Mueller-Hoissen
math.CO math-ph math.MP nlin.SI