Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The non-linear Schr\"odinger equation and the conformal properties of
  non-relativistic space-time   The cubic non-linear Schr\"odinger equation where the coefficient of the
nonlinear term is a function $F(t,x)$ only passes the Painlev\'e test of Weiss,
Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants.
This is explained by transforming the time-dependent system into the
constant-coefficient NLS by means of a time-dependent non-linear
transformation, related to the conformal properties of non-relativistic
space-time. A similar argument explains the integrability of the NLS in a
uniform force field or in an oscillator background.

31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an