Cloaking of the momentum in acoustic waves

Through an appropriate change in variables, we find that the three-dimensional acoustic wave equation is subject to the transformation media interpretation. In particular, we determine that this interpretation can be extended beyond the pressure difference to also account for the momentum transported by the wave. The suitability of momentum transport is especially interesting as it is an example where the field of interest is not governed by a wave equation. We examine how both fields behave in the case of cloaking. Explicit consideration of the boundary conditions shows that perfect cloaking is preserved, even when the incoming momentum is nonzero at the surface of the cloak.