Nonlinear q-Stokes phenomena for q-Painlevé I

@article{Joshi2018NonlinearQP,
  title={Nonlinear q-Stokes phenomena for q-Painlev{\'e} I},
  author={N. Joshi and C. Lustri and S. Luu},
  journal={Journal of Physics A},
  year={2018},
  volume={52},
  pages={065204}
}
We consider the asymptotic behaviour of solutions of the first $q$-difference Painlev\'{e} equation in the limits $|q|\rightarrow 1$ and $n\rightarrow\infty$. 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… Expand

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