NONEXISTENCE OF GAP SOLITONS IN NONLINEARLY COUPLED SYSTEMS

We consider a model consisting of two subsystems with crossing linear dispersion curves, in the case when the coupling between the subsystem s is purely nonlinear, so that the crossing does not give rise to a ga p in the linear spectrum. We demonstrate that there is a fairly genera l mechanism precluding the existence of (bright) solitons in systems o f this type.