Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trivalent Graphs and Solitons   It is shown that the fourth order real self-adjoint difference operator on
the Tivalent Tree admits nontrivial deformations preserving one energy level
and therefore defines a nontrinial hierarhy of the completely integrable
nonlinear systems representible through the ''L-A-B-triple''. The Laplace
transformations for these operators are also constructed. Nothing like that
exists for the second order difference operators on this tree.

3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph