Evolution of Coupled Scalar and Spinor Particles in Classical Field Theory

We study the evolution of mixed scalar as well as spinor fields within the context of the classical fields theory. The initial conditions problem is solved and the fields distributions, exactly accounting for the initial conditions, are obtained for both scalar and spinor fields. In the system of two coupled fields we consider the special case of the initial conditions which are rapidly oscillating functions. It is demonstrated that the energy densities, for the scalar fields, and the intensities, for the spinor fields, coincide with the usual transition and survival probabilities of neutrino flavor oscillations in vacuum