Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On compatible metrics and diagonalizability of non-locally
  bi-Hamiltonian systems of hydrodynamic type   We study bi-Hamiltonian systems of hydrodynamic type with non-singular
(semisimple) non-local bi-Hamiltonian structures and prove that such systems of
hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary
non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic
type, there exist local coordinates (Riemann invariants) such that all the
related matrix differential-geometric objects, namely, the matrix V^i_j(u) of
this system of hydrodynamic type, the metrics g^{ij}_1(u) and g^{ij}_2(u) and
the affinors (w_{1, n})^i_j(u) and (w_{2,n})^i_j(u) of the non-singular
non-local bi-Hamiltonian structure of this system, are diagonal in these local
coordinates. The proof is a natural consequence of the general results of the
theory of compatible metrics and the theory of non-local bi-Hamiltonian
structures developed earlier by the present author.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn