  Modeling of sound propagation in media with azimuthal variations of the
material parameters typically necessitates approximations. Useful methods, such
as the 3-D parabolic equation (PE) method, need verification by correct
reference solutions for well-defined test examples. The present paper utilizes
reference solutions for media with particular types of lateral sound-speed
variation, as a complement to common wedge and canyon examples with bathymetry
variation. Notably, the adiabatic approximation is exact for the particular
media under study, implying, however, that verification of mode coupling
remains. Wavenumber integration, for computation of modal expansion
coefficients, produces accurate solutions for the field and its spatial
derivatives in the 3-D case. Explicit expressions are typically available for
the wavenumber integrands in terms of Airy and exponential functions. For a
related 2-D case with azimuthal symmetry, Hankel functions appear instead of
exponentials, and the wavenumber integration drops out. The PE verification
focuses on comparing the two sides of the PE at insertion of appropriately
scaled Helmholtz-equation solutions.
