Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hydrodynamic-type systems describing 2-dimensional polynomially
  integrable geodesic flows   Starting from a homogeneous polynomial in momenta of arbitrary order we
extract multi-component hydrodynamic-type systems which describe 2-dimensional
geodesic flows admitting the initial polynomial as integral. All these
hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are
integrable according to the generalized hodograph method. Moreover, they are
integrable in a constructive sense as polynomial first integrals allow to
construct generating equations of conservation laws. According to the
multiplicity of the roots of the polynomial integral, we separate integrable
particular cases.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ