  We present integral-field spectroscopy of the ionized gas in the central
regions of four galaxies with a low surface brightness disk taken with the
Visible Multi Object Spectrograph at the Very Large Telescope and aimed at
testing the accuracy in the determination of the central logarithmic slope
$\alpha$ of the mass density radial profile $\rho(r) \propto r^\alpha$ in this
class of objects. For all the sample galaxies we subtracted from the observed
velocity field the best-fit model of gas in circular motions and derived the
residuals. Only ESO-LV 5340200 is characterized by a regular velocity field. We
extracted the velocity curves of this galaxy along several position angles, in
order to estimate the uncertainty in deriving the central gradient of the total
mass density from long-slit spectroscopy. We report the detection of strong
non-ordered motions of the ionized gas in three out of four sample galaxies.
The deviations have velocity amplitudes and spatial scales that make not
possible to disentangle between cuspy and core density radial profiles.
