Construction of a Lax Pair for the E6(1)q-Painlevé System

@article{Witte2012ConstructionOA,
  title={Construction of a Lax Pair for the E6(1)q-Painlev{\'e} System},
  author={Nicholas S. Witte and Christopher M. Ormerod},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2012},
  volume={8},
  pages={097}
}
  • N. Witte, C. Ormerod
  • Published 30 June 2012
  • Mathematics, Physics
  • Symmetry Integrability and Geometry-methods and Applications
We construct a Lax pair for the $E^{(1)}_6 $ $q$-Painleve system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the $q$-linear lattice - through a natural generalisation of the big $q$-Jacobi weight. As a by-product of our construction we derive the coupled first-order $q$-difference equations… 
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16 Citations
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6
Methods Citations
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16 Citations

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Citation Type

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Lax pairs of discrete Painlevé equations: (A2+A1)(1) case
  • N. Joshi, Nobutaka Nakazono
  • Mathematics, Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2016
In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlevé equations by using a reduced hypercube structure. In particular, we consider the A5(1)-surface…
Hypergeometric special solutions to additive difference Painlevé equations by Padé method
We have studied Pad\'e interpolation problems on an additive grid, related to additive difference ($d$-) Painlev\'e equations of type $E_7^{(1)}$, $E_6^{(1)}$, $D_4^{(1)}$ and $A_3^{(1)}$. By solving…
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