English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Matrix Kadomtsev–Petviashvili equation: Tropical limit, Yang–Baxter and pentagon maps

Dimakis, A., & Müller-Hoissen, F. (2018). Matrix Kadomtsev–Petviashvili equation: Tropical limit, Yang–Baxter and pentagon maps. Theoretical and Mathematical Physics, 196(2), 1164-1173. doi:10.1134/S0040577918080056.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/21.11116/0000-0002-975D-C Version Permalink: http://hdl.handle.net/21.11116/0000-0003-AAD0-2
Genre: Journal Article

Files

show Files

Locators

show

Creators

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

Content

show
hide
Free keywords: soliton, KP equation, Yang–Baxter map, pentagon equation, hexagon equation, tropical limit, binary tree, dilogarithm
 Abstract: In the tropical limit of matrix KP-II solitons, their support at fixed time is a planar graph with "polarizations" attached to its linear parts. In this work we explore a subclass of soliton solutions whose tropical limit graph has the form of a rooted and generically binary tree, as well as solutions with a limit graph consisting of two relatively inverted such rooted tree graphs. The distribution of polarizations over the constituting lines of the graph is fully determined by a parameter-dependent binary operation and a (in general non-linear) Yang-Baxter map, which in the vector KP case becomes linear, hence is given by an R-matrix. The parameter-dependence of the binary operation leads to a solution of the pentagon equation, which exhibits a certain relation with the Rogers dilogarithm via a solution of the hexagon equation, the next member in the family of polygon equations. A generalization of the R-matrix, obtained in the vector KP case, is found to also solve a pentagon equation. A corresponding local version of the latter then leads to a new solution of the hexagon equation.

Details

show
hide
Language(s): eng - English
 Dates: 2018-09-042018-08
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1134/S0040577918080056
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Theoretical and Mathematical Physics
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 196 (2) Sequence Number: - Start / End Page: 1164 - 1173 Identifier: -