  We employ the Riemann-Hilbert problem for solution of the initial-boundary
value problems for nearly integrable equations on the half line which have
important applications in physics. The detailed derivation of the integrable
and perturbation-induced evolutions of the spectral data are given for the two
most important models, the self-induced transparency and the stimulated Raman
scattering. In particular, we prove that dephasing stabilizes the spike
phenomenon in the stimulated Raman scattering.
