Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Euler's elastica to the mKdV hierarchy, through the Faber
  polynomials   The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing
isometry and isoenergy conditions on a moduli space of plane loops. The
conditions are compared to the constraints that define Euler's elastica.
Moreover, the conditions are shown to be constraints on the curvature and other
invariants of the loops which appear as coefficients of the generating function
for the Faber polynomials.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
19
The categories of this paper are: eess
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio