  The scattering of two Dashen-Hasslacher-Neveu (DHN) baryons in the large N
Gross-Neveu model is solved exactly using the relativistic, time-dependent
Hartree-Fock approach. Unlike the special case of kink-antikink scattering, the
scattering of DHN baryons is sensitive to the back-reaction of the fermions
bound inside the baryons. Correspondingly the solution is much more complicated
than the kink-antikink scattering solutions, which can be expressed in terms of
sinh-Gordon solitons. Nevertheless, we present a simple ansatz form that gives
closed analytic expressions for both the space-time dependent mean fields and
the Dirac spinors for all continuum and bound states. The solution can also be
applied to the scattering of polarons and solitons in conducting polymers.
