Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integrable time-dependent non-linear Schr\"odinger equation   The cubic non-linear Schr\"odinger equation (NLS), where the coefficient of
the non-linear term can be a function $F(t,x)$, is shown to pass the Painlev\'e
test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$
constants. This is explained by transforming the time-dependent system into the
ordinary NLS (with $F=\const$.) by means of a time-dependent on-linear
transformation, related to the conformal properties of non-relativistic
space-time.

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th