Leontovich–Fock Parabolic Equation Method in the Neumann Diffraction Problem on a Prolate Body of Revolution

Creeping waves in the shadow region with the Dirichlet and Neumann conditions

“…A. S. Kirpichnikova and N. Ya. Kirpichnikova obtained the first three terms of the wave field approximation for the problem with Neumann boundary conditions [7,8]. The novelty of the present paper is in the description of the creeping waves in the shadow region for the Neumann problem.…”

Comparison of the currents in the Dirichlet and Neumann shortwave diffraction problems of a plane wave from smooth prolate bodies of revolution

“…Thus, due to the presence of the negative exponent in F (σ) and G(σ) in the shadow zone, the current in the shadow decays fast. Fock's formulae (3), (4) give continuous transition of the current from the lit zone to the shadow zone in both Dirichlet and Neumann problems [6]. Table below present the first three roots of the Airy function w 1 (ζ q ) = 0 and its derivative w 1 (ζ q ) = 0:…”

“…Consider the correction terms W 1 and W 2 in (1). Calculation of these terms requires time and effort [1,4]. The second large parameter Λ 0 = ρ0 f (0) appears to matter due to the shape of the scatterer, this parameter measures its prolongation.…”

“…We use the Fock-Leontovich parabolic equation method [1,4,6] to obtain the first three terms of the asymptotic expansion U = e iks W = e iks W 0 +…”

“…We call W 0 the main, W 1 the first correcting and W 2 the second correcting terms of the expansion. Expansions (1) have been obtained for both the Dirichlet [1] and the Neumann problems [4]. The field has been constructed in the vicinity of the light-shadow boundary, see zone 3 in Fig.…”