Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable boundary conditions for the Hirota-Miwa equation and Lie
  algebras   Systems of discrete equations on a quadrilateral graph related to the series
$D^{(2)}_N$ of the affine Lie algebras are studied. The systems are derived
from the Hirota-Miwa equation by imposing boundary conditions compatible with
the integrability property. The Lax pairs for the systems are presented. It is
shown that in the continuum limit the quad systems tend to the corresponding
systems of the differential equations belonging to the well-know
Drinfeld-Sokolov hierarchies. The problem of finding the formal asymptotic
expansion of the solutions to the Lax equations is studied. Generating
functions for the local conservation laws are found for the systems
corresponding to $D^{(2)}_3$. An example of the higher symmetry is presented.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th