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 field theory. The initial condition 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 of the scalar fields and the intensities of the spinor fields coincide with the usual transition and survival probabilities of neutrino flavor oscillations in vacuum.