Topology in Shallow-Water Waves: A Spectral Flow Perspective

In the context of topological insulators, shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For with a boundary, parameter space involves both longitudinal momentum and boundary conditions exhibits peculiar singularity. We resolve anomaly in question by defining new kind edge index as spectral flow around this Crucially, samples whole family conditions, we interpret it boundary-driven quantized pumping. Our is stable due nature flow, prove its correspondence bulk Chern number using scattering theory relative version Levinson’s theorem. The full structure also investigated.