  Our GBDT version of B\"acklund-Darboux transformation is applied to the
construction of wide classes of new explicit solutions of self-adjoint and
skew-self-adjoint Dirac systems, dynamical Dirac and Dirac--Weyl systems. That
is, we construct explicit solutions of systems with non-vanishing at infinity
potentials. In particular, the cases of steplike potentials and power growth of
potentials are treated. It is essential (especially, for dynamical case) that
the generalised matrix eigenvalues are used in GBDT instead of the usual
eigenvalues (and those matrix eigenvalues are not necessarily diagonal). The
connection of Dirac--Weyl system with graphene theory is discussed. Explicit
expressions for Weyl--Titchmarsh functions are derived.
