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  KP line solitons and Tamari lattices

Dimakis, A., & Müller-Hoissen, F. (2011). KP line solitons and Tamari lattices. Journal of Physics A: Mathematical and Theoretical, 44: 025203. doi:10.1088/1751-8113/44/2/025203.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-11F7-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-11F8-8
Genre: Journal Article

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 Creators:
Dimakis, Aristophanes, Author
Müller-Hoissen, Folkert1, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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 Abstract: The Kadomtsev–Petviashvili (KP) II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at 'critical' events where a transition to a different rooted binary tree takes place. We prove that these correspond to maximal chains in Tamari lattices (which are poset structures on associahedra). We further derive results that allow us to compute details of the evolution, including the critical events. Moreover, we present some insights into the structure of the more general line soliton solutions. All this yields a characterization of possible evolutions of line soliton patterns on a shallow fluid surface (provided that the KP-II approximation applies).

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Language(s): eng - English
 Dates: 2011
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: eDoc: 522421
DOI: 10.1088/1751-8113/44/2/025203
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Title: Journal of Physics A: Mathematical and Theoretical
  Alternative Title : J. Phys. A: Math. Theor.
Source Genre: Journal
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Pages: - Volume / Issue: 44 Sequence Number: 025203 Start / End Page: - Identifier: -