Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 -
  dimensional vector fields   We introduce a hierarchy of integrable PDEs in 2+1 dimensions arising from
the commutation of 2-dimensional vector fields. We also solve the associated
Cauchy problems, using the recently developed Inverse Scattering Transform for
1-parameter families of multidimensional vector fields.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom