TY - JOUR
T1 - DISCRETE SOLITONS IN INFINITE REDUCED WORDS
AU - Glick, Max
AU - Pylyavskyy, Pavlo
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type A. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized using Lusztig’s braid move (a, b, c) ↦ (bc/(a+c), a+c, ab/(a+c)). We use wiring diagrams on a cylinder to interpret chamber variables as τ-functions. This allows us to realize our systems as reductions of the Hirota bilinear difference equation and thus obtain N-soliton solutions.
AB - We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type A. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized using Lusztig’s braid move (a, b, c) ↦ (bc/(a+c), a+c, ab/(a+c)). We use wiring diagrams on a cylinder to interpret chamber variables as τ-functions. This allows us to realize our systems as reductions of the Hirota bilinear difference equation and thus obtain N-soliton solutions.
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U2 - 10.1007/s00031-018-9488-3
DO - 10.1007/s00031-018-9488-3
M3 - Article
AN - SCOPUS:85051470927
SN - 1083-4362
VL - 24
SP - 31
EP - 66
JO - Transformation Groups
JF - Transformation Groups
IS - 1
ER -