  Formation of fermion bag solitons is an important paradigm in the theory of
hadron structure. We report here on our non-perturbative analysis of this
phenomenon in the 1+1 dimensional massive Gross-Neveu model, in the large $N$
limit. Our main result is that the extremal static bag configurations are
reflectionless, as in the massless Gross-Neveu model. Explicit formulas for the
profiles and masses of these solitons are presented. We also present a
particular type of self-consistent reflectionless solitons which arise in the
massive Nambu-Jona-Lasinio models, in the large-N limit.
