KP solitons, higher Bruhat and Tamari orders

Details KP solitons, higher Bruhat and Tamari orders KP solitons, higher Bruhat and Tamari orders

2011-10-16

arxiv.org/abs/1110.3507v2

Mathematics

Combinatorics

28 pages, 25 figures, 2nd version: some corrections and changes in section 4, Tamari Memorial Festschrift

Scientific paper

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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