Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux Transformations for orthogonal differential systems and
  differential Galois Theory   Darboux developed an algebraic mechanism to construct an infinite chain of
"integrable" second order differential equations as well as their solutions.
After a surprisingly long time, Darboux's results had important features in the
analytic context, for instance in quantum mechanics where it provides a
convenient framework for Supersymmetric Quantum Mechanics. Today, there are a
lot of papers regarding the use of Darboux transformations in various contexts,
not only in mathematical physics. In this paper, we develop a generalization of
the Darboux transformations for tensor product constructions on linear
differential equations or systems. Moreover, we provide explicit Darboux
transformations for $\sym^2 (\mathrm{SL}(2,\mathbb{C}))$ systems and, as a
consequence, also for $\mathfrak{so}(3, C_K)$ systems, to construct an infinite
chain of integrable (in Galois sense) linear differential systems. We introduce
SUSY toy models for these tensor products, giving as an illustration the
analysis of some shape invariant potentials.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con