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We prove stability and exponential convergence of the Perfectly Matched Layer(PML) method for acoustic scattering on manifolds with axial analyticquasicylindrical ends. These manifolds model long-range geometric perturbations(e.g. bending or stretching) of tubular waveguides filled with homogeneous orinhomogeneous media.  We construct non-reflective infinite PMLs replacing the metric on a part ofthe manifold by a non-degenerate complex symmetric tensor field. We prove thatthe problem with PMLs of finite length is uniquely solvable and solutions tothis problem locally approximate scattered solutions with an error thatexponentially tends to zero as the length of PMLs tends to infinity.

Analysis of Perfectly Matched Layer operators for acoustic scattering on manifolds with quasicylindrical ends