  We investigate non-diffracting hollow-core nonlinear optical waves
propagating in a layered nanoscaled metal-dielectric structure characterized by
a very small average linear dielectric permittivity (Nonlinear
Epsilon-Near-Zero metamaterial). We analytically show that hollow-core waves
have a power flow exactly vanishing at a central region and exhibiting a sharp
sloped profile at the edges of the regions surrounding the core. Physically,
the absence of power flow at the core region is due to the vanishing of the
transverse component of the electric displacement field, condition that can be
satisfied by the full compensation between the nonlinear and linear dielectric
contribution.
