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The light curves (LC) for Supernova (SN) can be modeled adopting theconversion of the flux of kinetic energy into radiation. This conversionrequires an analytical or a numerical law of motion for the expanding radius ofthe SN. In the framework of conservation of energy for the thin layerapproximation we present a classical trajectory based on a power law profilefor the density, a relativistic trajectory based on the Navarro--Frenk--Whiteprofile for the density, and a relativistic trajectory based on a power lawbehaviour for the swept mass. A detailed simulation of the LC requires theevaluation of the optical depth as a function of time. We modeled the LC ofSN~1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB060729 in the keV region. The time dependence of the magnetic field ofequipartition is derived from the theoretical formula for the luminosity.

Energy Conservation in the thin layer approximation: IV. The light curve for supernovae