  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.
