  We consider the nonrelativistic model of coupling bare discrete states with
continuum states in which the continuum states can have interactions among
themselves. By partial-wave decomposition and constraint to the conserved
angular momentum eigenstates, the model can be reduced to Friedrichs-like model
with additional interactions between the continua. If a kind of factorizable
form factor is chosen, the model can be exactly solvable, that is, the
generalized discrete eigenstates including bound states, virtual states, and
resonances, can all be represented using the original bare states, and so do
the in-state and out-state. The exact $S$ matrix is thus obtained. We then
discuss the behaviors of the dynamically generated $S$-wave and $P$-wave
discrete states as the coupling is varying when there is only one
self-interacting bare continuum state. We find that even when the potential is
repulsive there could also be resonances and virtual states. In the $P$-wave
cases with attractive interaction, we find that when there is a near-threshold
bound state, there will always be an accompanying virtual state and we also
give a more general argument of this effect.
