  We show theoretically that a photonic topological insulator can support edge
solitons that are strongly self-localized and propagate unidirectionally along
the lattice edge. The photonic topological insulator consists of a Floquet
lattice of coupled helical waveguides, in a medium with local Kerr
nonlinearity. The soliton behavior is strongly affected by the topological
phase of the linear lattice. The topologically nontrivial phase gives a
continuous family of solitons, while the topologically trivial phase gives an
embedded soliton that occurs at a single power, and arises from a self-induced
local nonlinear shift in the inter-site coupling. The solitons can be used for
nonlinear switching and logical operations, functionalities that have not yet
been explored in topological photonics. We demonstrate using solitons to
perform selective filtering via propagation through a narrow channel, and using
soliton collisions for optical switching.
