Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hydrodynamic integrability via geometry   This paper develops a geometric approach to the theory of integrability by
hydrodynamic reductions to establish an equivalence, for a large class of
quasilinear systems, between hydrodynamic integrability and the existence of
nets compatible with the geometry induced on the codomain of the system. This
unifies and extends known results for three subclasses of such systems. The
generalization is obtained by studying the algebraic geometry of the
characteristic correspondence of the system, and by introducing a generalized
notion of conjugate nets.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int