Edge waves on the boundary of vortex matter
Vortex matter is a dense uniform liquid assembly of same sense vortices in incompressible two-dimensional flow, a turbulent flows with sign-like eddies. I discuss two novel phenomena (i) a boundary layer of vorticity (vorticity layer), and (ii) a nonlinear wave propagating within the vorticity layer, the edge wave. Both are lost if the vortex matter is approximated as a continuous vorticity patch. The edge wave is governed by the integrable Benjamin-Davis-Ono equation exhibiting solitons with a quantized total vorticity and identified with the action of the Virasoro-Bott group, the centrally extended diffeomorphisms of the circle. The boundary wave is a hydrodynamic analog of the edge states of the fractional quantum Hall effect.