  We study the evolution of the coupled scalar and fermion fields within the
classical field theory. We examine the case of N coupled fields in 1+3
dimensional space. The general expressions for the fields distributions are
obtained. The particular case of two fields in 1+1 dimensional space is
carefully studied. We obtain the expressions for the averaged fields
intensities and show that in the relativistic limit they are similar to the
usual transition probabilities formulae of neutrino oscillations.
