Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-exactly solvable models in nonlinear optics   We study a large class of models with an arbitrary (finite) number of degrees
of freedom, described by Hamiltonians which are polynomial in bosonic creation
and annihilation operators, and including as particular cases n-th harmonic
generation and photon cascades. For each model, we construct a complete set of
commuting integrals of motion of the Hamiltonian, fully characterize the common
eigenspaces of the integrals of motion, and show that the action of the
Hamiltonian in these common eigenspaces can be represented by a quasi-exactly
solvable reduced Hamiltonian, whose expression in terms of the usual generators
of sl(2) is computed explicitly.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex