Leontovich–Fock parabolic equation method in the Neumann diffracion problem on a prolate body of revolution

This paper continues the series of publications on the shortwave diffraction of the plane wave on the prolate bodies of revolution with axial symmetry in Neumann problem. The approach which is based on Leontovich–Fock parabolic equation method for the two parameter asymptotic expansion of the solution is briefly described. Two correction terms are found for the Fock's main integral term of the solution expansion in the boundary layer. This solution can be continuously transformed into the ray solution in the lit zone and decays exponentially in the shadow zone. If the observation point is in the shadow zone near the scatterer, then the wave field can be obtained with the help of residue theory for the integrals of the reflected field, because the incident field does not reach the shadow zone. The obtained residues are necessary for the unique construction of the creeping waves in the boundary layer of the scatterer in the shadow zone.