  Understanding of the interaction of antiferromagnetic solitons including
domain walls and skyrmions with boundaries of chiral antiferromagnetic slabs is
important for the design of prospective antiferromagnetic spintronic devices.
Here, we derive the transition from spin lattice to micromagnetic nonlinear
$\sigma$-model with the corresponding boundary conditions for a chiral cubic
G-type antiferromagnet and analyze the impact of the slab boundaries and
antisymmetric exchange (Dzyaloshinskii--Moriya interaction) on the vector order
parameter. We apply this model to evaluate modifications of antiferromagnetic
domain walls and skyrmions upon interaction with boundaries for different
strengths of the antisymmetric exchange. Due to the presence of the
antisymmetric exchange, both types of antiferromagnetic solitons become broader
when approaching the boundary and transform to a mixed Bloch--N\'{e}el
structure. Both textures feel the boundary at the distance of about 5 magnetic
lengths. In this respect, our model provides design rules for antiferromagnetic
racetracks, which can support bulk-like properties of solitons.
