  Nonlinear Schr\"{o}dinger equation was originally derived in nonlinear optics
as a model for beam propagation, which naturally requires its application in
cylindrical coordinates. However, the derivation was done in the Cartesian
coordinates with the Laplacian $\Delta_{\perp} = \partial_{x}^{2} +
\partial_{y}^{2}$ transverse to the beam $z$-direction tacitly assumed to be
covariant. As we show, first, with a simple example and, next, with a
systematic derivation in cylindrical coordinates, $\Delta_{\perp} =
\partial_{r}^{2} + \frac{1}{r} \partial_{r}$ must be amended with a potential
$V(r)=-\frac{1}{r^{2}}$, which leads to a Gross-Pitaevskii equation instead.
Hence, the beam dynamics and collapse must be revisited.
