  We study the cubic-quintic NLS in three space dimensions. It is known that
scattering holds for solutions with mass-energy in a region corresponding to
positive virial, the boundary of which is delineated both by ground state
solitons and by certain rescalings thereof. We classify the possible behaviors
of solutions on the part of the boundary attained solely by solitons. In
particular, we show that non-soliton solutions either scatter in both time
directions or coincide (modulo symmetries) with a special solution, which
scatters in one time direction and converges exponentially to the soliton in
the other.
