  Non-perturbative phenomena in four-wave mixing spectra of semiconductors are
studied using the exact solution of a widely used phenomenological non-linear
equation of motion of the exciton polarization. It is shown that Coulomb
interaction, included in the nonlinearity, leads to two characteristic effects,
which are essentially of dynamical origin, -- a split of the exciton peak and a
non-monotonous dependence of the response at the exciton frequency on the
magnitude of the external field. Relations between the spectral features and
the parameters of the system is obtained. It is found that the transition from
perturbative to non-perturbative regimes is controlled by parameters inversely
proportional to the decay rate. It implies that the condition of low excitation
density does not necessarily warrant applicability of the perturbational
approach.
