  A salient feature of solid-state topological materials in two dimensions is
the presence of conducting electronic edge states that are insensitive to
scattering by disorder. Such unidirectional edge states have been explored in
many experimental settings beyond solid-state electronic systems, including in
photonic devices, mechanical and acoustic structures, and others. It is of
great interest to understand how topological states behave in the presence of
inter-particle interactions and nonlinearity. Here we experimentally
demonstrate unidirectional soliton-like nonlinear states on the edge of
photonic topological insulators consisting of laser-written waveguides. As a
result of the optical Kerr nonlinearity of the ambient glass, the soliton-like
wavepacket forms a non-diffracting coherent structure that slowly radiates
power because of the intrinsic gaplessness of the system. The realization of
soliton-like edge states paves the way to an understanding of topological
phenomena in nonlinear systems and those with inter-particle interactions.
