Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Similarity reductions and new nonlinear exact solutions for the 2D
  incompressible Euler equations   For the 2D and 3D Euler equations, their existing exact solutions are often
in linear form with respect to variables x,y,z. In this paper, the
Clarkson-Kruskal reduction method is applied to reduce the 2D incompressible
Euler equations to a system of completely solvable ordinary equations, from
which several novel nonlinear exact solutions with respect to the variables x
and y are found.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg