Abstract
A hierarchy of the 3D coupled parabolic equations is derived by the method of multiple scales. The solutions of the derived equations represent the successive terms in an asymptotic expansion of the solution of the 3D Helmholtz equation. The equations are complemented with the consistent interface and boundary conditions. The Cauchy initial conditions for the parabolic equations are set up in such a way that the solution in the far field approximates the solution of the Helmholtz equation in the unbounded 3D space. The derived parabolic equations are used to solve a problem of the propagation in a perfect 3D wedge. The comparison to the image source solutions is used for the validation of the proposed parabolic approximation.
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