Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the singularity structure of the discrete KdV equation   The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is
often thought to possess the singularity confinement property because it
confines on an elementary quadrilateral. Here we investigate the singularity
structure of the dKdV equation through reductions of the equation, obtained for
initial conditions on a staircase with height 1, and show that it is much more
subtle than one might assume. We first study the singularities for the mappings
obtained after reduction and contrast these with the singularities that arise
in non-integrable generalizations of those mappings. We then show that the
so-called `express method' for obtaining dynamical degrees for second order
mappings can be succesfully applied to all the higher order mappings we
derived. Finally, we use the information obtained on the singularity structure
of the reductions to describe an important subset of singularity patterns for
the dKdV equation and we present an example of a non-confining pattern and
explain why its existence does not contradict the integrability of the dKdV
equation.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg