Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear $q$-Stokes phenomena for $q$-Painlev\'{e} I   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 mathematical descriptions of the
rapid switching behaviour associated with Stokes curves. Through this analysis,
we also determine the regions of the complex plane in which the asymptotic
behaviour is described by a power series expression, and find that the Stokes
curves are described by curves known as $q$-spirals.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci