  Topological photonics has emerged recently as a novel approach for realizing
robust optical circuitry, and the study of nonlinear effects in topological
photonics is expected to open the door for tunability of photonic structures
with topological properties. Here, we study the topological edge states and
topological gap solitons which reside in the same bandgaps described by the
nonlinear Dirac model, in both one- and two-dimensions. We reveal strong
nonlinear interaction between those dissimilar topological modes manifested in
the excitation of the topological edge states by scattered gap solitons.
Nonlinear tunability of localized states is explicated with exact analytical
solutions for the two-component spinor wave function. Our studies are
complemented by spatiotemporal numerical modeling of the wave transport in one-
and two-dimensional topological systems.
