Nonlinear q-Stokes phenomena for q-Painlevé I

  title={Nonlinear q-Stokes phenomena for q-Painlev{\'e} I},
  author={Nalini T. Joshi and Christopher J. Lustri and S. Luu},
  journal={Journal of Physics A: Mathematical and Theoretical},
We consider the asymptotic behavior of solutions of the first -difference Painlevé equation in the limits and . Using asymptotic power series, we describe four families of solutions that contain free parameters hidden beyond-all-orders. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. In order to investigate such phenomena we apply exponential asymptotic techniques to obtain mathematical descriptions of the rapid switching… 

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