English

Quadrirational Yang-Baxter maps and the affine-E8 Painleve lattice

Exactly Solvable and Integrable Systems 2014-05-13 v1 Mathematical Physics math.MP

Abstract

We establish that the quadrirational Yang-Baxter maps, considered on their symmetry-complete lattice, give an un-normalized form of the Painleve systems associated with affine-E8 symmetry. This is a unified representation bringing KdV-type and Painleve-type systems together outside of the usual paradigm of reductions. Our approach exploits the geometric characterisation of the Painleve equations and the formulation of both kinds of systems in terms of birational groups.

Keywords

Cite

@article{arxiv.1405.2745,
  title  = {Quadrirational Yang-Baxter maps and the affine-E8 Painleve lattice},
  author = {James Atkinson and Yasuhiko Yamada},
  journal= {arXiv preprint arXiv:1405.2745},
  year   = {2014}
}

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20 pages