Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the symmetric formulation of the Painleve IV equation   Symmetries and solutions of the Painleve IV equation are presented in an
alternative framework which provides the bridge between the Hamiltonian
formalism and the symmetric Painleve IV equation. This approach originates from
a method developed in the setting of pseudo-differential Lax formalism
describing AKNS hierarchy with the Darboux-Backlund and Miura transformations.
  In the Hamiltonian formalism the Darboux-Backlund transformations are
introduced as maps between solutions of the Hamilton equations corresponding to
two allowed values of Hamiltonian's discrete parameter. The action of the
generators of the extended affine Weyl group of the $A_2$ root system is
realized in terms of three "square-roots" of such Darboux-Backlund
transformations defined on a multiplet of solutions of the Hamilton equations.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph