  We theoretically explore the dynamics of spatial solitons in
nonlinear/interacting bosonic topological insulators. We employ a time-reversal
broken Lieb-lattice analog of a Chern insulator and find that in the presence
of a saturable nonlinearity, solitons bifurcate from a band of non-zero Chern
number into the topological band gap with vortex-like structure on a
sublattice. We numerically demonstrate the existence stable vortex solitons for
a range of parameters and that the lattice soliton dynamics are subject to the
anomalous velocity associated with large Berry curvature at the topological
Lieb band edge. The features of the vortex solitons are well described by a new
underlying continuum Dirac model. We further show a new kind of interaction:
when these topological solitons `bounce' off the edge of a finite structure,
they create chiral edge states, and this give rise to an "anomalous" reflection
of the soliton from the boundary.
