Resonant scattering of solitons

We study the scattering of solitons in the nonlinear Schr?dinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The analytical predictions are tested numerically in regimes characterized by various time scales. Special attention is paid to intermode interactions and their effect on coherence, decoherence, and dephasing of plane-wave modes which build up the soliton.