Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Discrete Painleve Equations Associated with the Lattice KdV Systems
  and the Painleve VI Equation   A new integrable nonautonomous nonlinear ordinary difference equation is
presented which can be considered to be a discrete analogue of the Painleve V
equation. Its derivation is based on the similarity reduction on the
two-dimensional lattice of integrable partial difference equations of KdV type.
The new equation which is referred to as GDP (generalised discrete Painleve
equation) contains various ``discrete Painleve equations'' as subcases for
special values/limits of the parameters, some of which were already given
before in the literature. The general solution of the GDP can be expressed in
terms of Painleve VI (PVI) transcendents. In fact, continuous PVI emerges as
the equation obeyed by the solutions of the discrete equation in terms of the
lattice parameters rather than the lattice variables that label the lattice
sites. We show that the bilinear form of PVI is embedded naturally in the
lattice systems leading to the GDP. Further results include the establishment
of Baecklund and Schlesinger transformations for the GDP, the corresponding
isomonodromic deformation problem, and the self-duality of its bilinear scheme.

2
The categories of this paper are: math
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc