Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The symmetry approach to integrability: recent advances   We provide a concise introduction to the symmetry approach to integrability.
Some results on integrable evolution and systems of evolution equations are
reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We
further describe non-abelian integrable equations, especially matrix (ODE and
PDE) systems. Some non-evolutionary integrable equations are studied using a
formulation of formal recursion operators that allows to study
non-diagonalisable systems of evolution equations.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: math
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio