Accurate numerical solutions are presented for benchmark problems associated with propagation in a wedge with different bottom boundary conditions as well as in a plane-parallel waveguide with changing profile with range. The benchmark problems are solved with three different general-purpose numerical codes: (1) a coupled-mode code providing a full-spectrum two-way (backscatter included) solution of the wave equation, (2) a finite-difference PE code providing a wide-angle solution of the one-way parabolic approximation of the wave equation, and (3) a split-step PE code providing a more narrow-angle solution of the one-way parabolic approximation of the wave equation. Only the two-way coupled-mode results can be considered accurate solutions of the benchmark problems.
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Jensen et al. (1990) studied this question.