Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete exponential type systems on a quad graph, corresponding to the
  affine Lie algebras $A^{(1)}_{N-1}$   The article deals with the problem of the integrable discretization of the
well-known Drinfeld-Sokolov hierarchies related to the Kac-Moody algebras. A
class of discrete exponential systems connected with the Cartan matrices has
been suggested earlier in \cite{GHY} which coincide with the corresponding
Drinfeld-Sokolov systems in the continuum limit. It was conjectured that the
systems in this class are all integrable and the conjecture has been approved
by numerous examples. In the present article we study those systems from this
class which are related to the algebras $A^{(1)}_{N-1}$. We found the Lax pair
for arbitrary $N$, briefly discussed the possibility of using the method of
formal diagonalization of Lax operators for describing a series of local
conservation laws and illustrated the technique using the example of $N=3$.
Higher symmetries of the system $A^{(1)}_{N-1}$ are presented in both
characteristic directions. Found recursion operator for $N=3$. It is
interesting to note that this operator is not weakly nonlocal.

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The categories of this paper are: comp-gas
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph