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KP solitons, higher Bruhat and Tamari orders

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Müller-Hoissen,  Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Müller-Hoissen, F., & Dimakis, A. (2012). KP solitons, higher Bruhat and Tamari orders. In F. Müller-Hoissen, J. M. Pallo, & J. Stasheff (Eds.), Associahedra, Tamari Lattices and Related Structures (pp. 391-423). Basel: Birkhäuser, Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1123-6
Abstract
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.