The cubic non-linear Schrödinger equation (NLS), where the coefficient of the non-linear term can be a function F(t,x), is shown to pass the Painlevé test of Weiss, Tabor, and Carnevale only for F=(a+bt)−1, where a
Nearby in the stack
and
b
constants. This is explained by transforming the time-dependent system into the ordinary NLS (with
F=
.) by means of a time-dependent on-linear transformation, related to the conformal properties of non-relativistic space-time.