Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii
  equation II   In this paper, we proceed along our analysis of the Korteweg-de Vries
approximation of the Gross-Pitaevskii equation initiated in a previous paper.
At the long-wave limit, we establish that solutions of small amplitude to the
one-dimensional Gross-Pitaevskii equation split into two waves with opposite
constant speeds $\pm \sqrt{2}$, each of which are solutions to a Korteweg-de
Vries equation. We also compute an estimate of the error term which is somewhat
optimal as long as travelling waves are considered. At the cost of higher
regularity of the initial data, this improves our previous estimate.

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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess