Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the integrability of symplectic Monge-Amp\'ere equations   Let u be a function of n independent variables x^1, ..., x^n, and U=(u_{ij})
the Hessian matrix of u. The symplectic Monge-Ampere equation is defined as a
linear relation among all possible minors of U. Particular examples include the
equation det U=1 governing improper affine spheres and the so-called heavenly
equation, u_{13}u_{24}-u_{23}u_{14}=1, describing self-dual Ricci-flat
4-manifolds. In this paper we classify integrable symplectic Monge-Ampere
equations in four dimensions (for n=3 the integrability of such equations is
known to be equivalent to their linearisability). This problem can be
reformulated geometrically as the classification of 'maximally singular'
hyperplane sections of the Plucker embedding of the Lagrangian Grassmannian. We
formulate a conjecture that any integrable equation of the form F(u_{ij})=0 in
more than three dimensions is necessarily of the symplectic Monge-Ampere type.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas