  A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave
equation in the whole real axis and numerical discretization is designed for
solving the reduced PML problem on a bounded domain. The nonlocal PML poses
challenges not faced in PDEs. For example, there is no derivative in nonlocal
models, which makes it impossible to replace derivates with complex ones. Here
we provide a way of constructing the PML for nonlocal models, which decays the
waves exponentially impinging in the layer and makes reflections at the
truncated boundary very tiny. To numerically solve the nonlocal PML problem, we
design the asymptotically compatible (AC) scheme for spatially nonlocal
operator by combining Talbot's contour, and a Verlet-type scheme for time
evolution. The accuracy and effectiveness of our approach are illustrated by
various numerical examples.
