Classifying topological solitons using local markers

Due to the local nature of the nonlinearities in nonlinear photonic topological insulators, attempts to describe its topology using traditional band structure approaches are not suitable. Here, we propose to use the so[1]called spectral localizer, which allows us to define local topological invariants such as a local Chern number. Using the nonlinear Haldane model with on-site Kerr terms, we show that the soliton can creates topological interfaces inside the lattice.