Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the intermediate integral for Monge-Ampere equations   Goursat showed that in the presence of an intermediate integral, the problem
of solving a second-order Monge-Ampere equation can be reduced to solving a
first-order equation, in the sense that the generic solution of the first-order
equation will also be a solution of the original equation. An attempt by
Hermann to give a rigorous proof of this fact contains an error; we show that
there exists an essentially unique counterexample to Hermann's assertion and
state and prove a correct theorem.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom