Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Burgers equation and the Korteweg-de Vries equation with quadratic
  nonlinearity   We study generalized variants of the Burgers equation and the KdV equation on
the circle. The main goal of the paper is to show that both extensions can be
recast as geodesic equations on a suitable diffeomorphism group of the circle
and the corresponding Bott-Virasoro group respectively. As a consequence we
obtain that the initial value problem for the Burgers equation with an
additional quadratic term is well-posed on a scale of Sobolev spaces on the
circle.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph