Solitons and quantization in nonlinear topological systems

The description of the topological properties of condensed matter, photonic, or other wave systems is most natural in the linear (i.e., non-interacting) domain, where invariants such as the Chern number can be described as integrals over momentum space. Here we discuss several experiments on nonlinear topological systems, including the observation of optical spatial solitons therein, as well as the integer and fractional quantization of soliton motion in Thouless pumps.