  We analyze the 1+1 dimensional Nambu-Jona-Lasinio model non-perturbatively.
We study non-trivial saddle points of the effective action in which the
composite fields $\sigx=<\bar\psi\psi>$ and $\pix=<\bar\psii\gam_5\psi>$ form
static space dependent configurations. These configurations may be viewed as
one dimensional chiral bags that trap the original fermions (``quarks'') into
stable extended entities (``hadrons''). We provide explicit expressions for the
profiles of some of these objects and calculate their masses. Our analysis of
these saddle points, and in particular, the proof that the $\sigx, \pix$
condensations must give rise to a reflectionless Dirac operator, appear to us
simpler and more direct than the calculations previously done by Shei, using
the inverse scattering method following Dashen, Hasslacher, and Neveu.
