Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bethe ansatz and inverse scattering transform in a periodic box-ball
  system   We formulate the inverse scattering method for a periodic box-ball system and
solve the initial value problem. It is done by a synthesis of the combinatorial
Bethe ansa"tze at q=1 and q=0, which provides the ultradiscrete analogue of
quasi-periodic solutions in soliton equations, e.g., action-angle variables,
Jacobi varieties, period matrices and so forth. As an application we establish
explicit formulas counting the states characterized by conserved quantities and
the generic and fundamental period under the commuting family of time
evolutions.

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The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg