The Leontovich−Fock Parabolic Equation Method in Problems of Short-Wave Diffraction by Prolate Bodies

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

“…1). The solution there is constructed by the Leontovich-Fock parabolic equation method, see [1,5,7]. The first three terms of the following expansion were constructed in the boundary layer 2 for both Dirichlet and Neumann problems ( [5,7]): To this end, the stretched dimensionless coordinates…”

“…N. Ya. Kirpichnikova and M. M. Popov described the diffracted field for the problem with the Dirichlet boundary conditions [5,6]. A. S. Kirpichnikova and N. Ya.…”

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

“…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.…”