Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian and Hamiltonian Structures for the Constant Astigmatism
  Equation   In this paper we found a Lagrangian representation and corresponding
Hamiltonian structure for the constant astigmatism equation. Utilizing this
Hamiltonian structure and extra conservation law densities we construct a first
evolution commuting flow of the third order. Also, we apply the recursion
operator and present a second Hamiltonian structure. This bi-Hamiltonian
structure allows to replicate infinitely many local commuting flows and
corresponding local conservation law densities.

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph