Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integrable generalization of the Toda law to the square lattice   We generalize the Toda lattice (or Toda chain) equation to the square
lattice; i.e., we construct an integrable nonlinear equation, for a scalar
field taking values on the square lattice and depending on a continuous (time)
variable, characterized by an exponential law of interaction in both discrete
directions of the square lattice. We construct the Darboux-Backlund
transformations for such lattice, and the corresponding formulas describing
their superposition. We finally use these Darboux-Backlund transformations to
generate examples of explicit solutions of exponential and rational type. The
exponential solutions describe the evolution of one and two smooth
two-dimensional shock waves on the square lattice.

29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int