  Higher-order topological insulators (HOTI) are a novel topological phase
beyond the framework of the conventional bulk-boundary correspondence. In these
peculiar systems, the topologically nontrivial boundary modes are characterized
by a co-dimension of at least two. Despite several promising preliminary
considerations regarding the impact of nonlinearity in such systems, the
flourishing field of experimental HOTI research has thus far been confined to
the linear evolution of topological states. As such, the observation of the
interplay between nonlinearity and the dynamics of higher-order topological
phases in conservative systems remains elusive. In our work, we experimentally
demonstrate nonlinear higher-order topological corner states. Our photonic
platform enables us to observe nonlinear topological corner states as well as
the formation of solitons in such topological structures. Our work paves the
way towards the exploration of topological properties of matter in the
nonlinear regime, and may herald a new class of compact devices that harnesses
the intriguing features of topology in an on-demand fashion.
