  Observations from the last decade have indicated the existence of a general
class of superluminous supernovae (SLSNe), in which the peak luminosity exceeds
10^{44} erg/s. Here we focus on a subclass of these events, where the light
curve is also tens of days wide, so the total radiated energy is order 10^{51}
erg. If the origin of these SLSNe is a core-collapse-driven explosion of a
massive star, then the mechanism which converts the explosion energy into
radiation must be very efficient (much more than in typical core collapse SNe,
where this efficiency is of order one percent). We examine the scenario where
the radiated luminosity is due to efficient conversion of kinetic energy of the
ejected stellar envelope into radiation by interaction with an optically thick,
pre-existing circumstellar material (CSM), presumably the product of a steady
wind from the progenitor. We base the analysis on a simple, numerically solved,
hydrodynamic diffusion model, which allows us to identify the qualitative
behavior of the observable light curves, and to relate them to the parameters
of the wind. We specifically show that a wide and superluminous supernova
requires the mass of the relevant wind material to be comparable to that of
ejected material from the exploding progenitor. We find the wind parameters
which explain the peak luminosity and width of the bolometric light curves of
three particular SLSNe, namely, SN 2005ap, SN 2006gy, and SN 2010gx, and show
that they are best fitted with a wind that extends to a radius of order 10^{15}
cm. These results serve as an additional indication that at least some SLSNe
are powered by interaction of the ejected material with a steady wind of
similar mass.
