  A new method to find the propagation equation system governing the scattering
of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let
the effects appear spontaneously, deleting as far as possible the
phenomenological ideas. In this way, we obtain propagation equation systems
that encodes several nonlinear effects. Once these systems obtained, the
numerical values of the tensors that characterize the answer of the medium to
an electromagnetic perturbation give weights to the different effects. This aim
is partly reached in this study, especially when treating harmonic generations.
For this, we start from the Maxwell's equation and give rigorously all the
hypothesis needed to attain equation systems that can be solved, at least from
a numerical point of view. Finally, a symmetry on the susceptibility tensors
that ensures that a medium is lossless from the electromagnetic point of view
is worked out.
