Energy Conservation in the thin layer approximation: IV. The light curve
  for supernovae
  The light curves (LC) for Supernova (SN) can be modeled adopting the
conversion of the flux of kinetic energy into radiation. This conversion
requires an analytical or a numerical law of motion for the expanding radius of
the SN. In the framework of conservation of energy for the thin layer
approximation we present a classical trajectory based on a power law profile
for the density, a relativistic trajectory based on the Navarro--Frenk--White
profile for the density, and a relativistic trajectory based on a power law
behaviour for the swept mass. A detailed simulation of the LC requires the
evaluation of the optical depth as a function of time. We modeled the LC of
SN~1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB
060729 in the keV region. The time dependence of the magnetic field of
equipartition is derived from the theoretical formula for the luminosity.
