Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite energy traveling waves for the Gross-Pitaevskii equation in the
  subsonic regime   In this paper we study the existence of finite energy traveling waves for the
Gross-Pitaevskii equation. This problem has deserved a lot of attention in the
literature, but the existence of solutions in the whole subsonic range was a
standing open problem till the work of Maris in 2013. However, such result is
valid only in dimension 3 and higher. In this paper we first prove the
existence of finite energy traveling waves for almost every value of the speed
in the subsonic range. Our argument works identically well in dimensions 2 and
3.
  With this result in hand, a compactness argument could fill the range of
admissible speeds. We are able to do so in dimension 3, recovering the
aforementioned result by Maris. The planar case turns out to be more difficult
and the compactness argument works only under an additional assumption on the
vortex set of the approximating solutions.

33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph