**DAY on DIFFRACTION
PROCEEDINGS**

**May 29 - June 1, 2000
St.Petersburg, Russia**

**The seminar is sponsored by: **

**
Russian Foundation for Basic Research
** **IEEE
Antennas and Propagation Society**

**(C) Day on Diffraction, Faculty of Physics,
SPbU, 2000**
**IEEE Catalog Number: 00EX450**
**ISBN 5-7997-0252-4**
**Print run 200**

** 70 years to V. M. Babich **

**On June 13, 2000 the family, friends and colleagues celebrated
the 70-th anniversary
of Professor Vassilii Mikhailovich Babich.**

Professor V. M. Babich is one of the leaders of the St. Petersburg Diffraction
School. He is worldwide recognized for his outstanding contributions to areas as diverse as the
diffraction and propagation of waves, elasticity, geophysics and partial differential
equations. He is an author of about 115 scientific papers and of 5 monographs of
which

**Boundary Layer Methods in Diffrac Problems
(with N. Ya. Kirpichnikova), ****Springer 1979**

**Short-Wavelength Diffraction Theory (with V. S.
Buldyrev),
Springer 1991**

**The Space--Time Ray Method
(with V. S. Buldyrev and I. A. Molotkov) , Cambridge University Press 1999**

**are avaiablel in English.**

**V. M. Babich is a member of the Editorial Boards of Wave Motion and of
St. Pe Mathematical Journal and the Editor of the series ``Mathematical Problems of Wave Propagation
Theory'' in Zapiski Nauch. Semin. POMI (Proceedings of Seminars at St. Petersburg Branch of the Steklov
Mathematical Institute) translated to English in Journal of Mathematical Sciences . He is a winner of the Soviet State Prize (1982) and of the
Fock's Prize of Russian Academy of Sciences (1998).**

**From 1967 he has been the Head of the Laboratory of Mathematical Problems in
Geophysics at St.Petersburg Branch of the Steklov Mathematical Institute and a Professor of the Department of Mathematical Physics at
St. Petersburg State University. During all these years Professor Babich has been having an amazing research
productivity, which he manages to combine with raising young researchers, teaching and successfully running a weekly St. Petersburg diffraction
seminar. He approached his anniversary travelling a lot, being as always
productive, energetic, full of ideas and plans.
His current research activity includes waves guided by curved structures, real and complex rays and diffraction by cones and elastic
wedges.**

**Despite his unbelievably intensive schedule, being also a head of a large family, having four
grandchildren, he remains at the same time easily accessible and always finds time and enjoys socializing with his numerous friends and
colleagues. On behalf of the participants of the DD'2000 and of all his colleagues
working in the diffraction theory we wish him good health. We are all looking forward to him continuing to
inspire us by his new ideas and remaining the leader of St. Petersburg
diffraction.**

**I.V.Andronov
Diffraction of hydroacoustic wave by a short joint of two semi-infinite elastic
plates................................ 7
A.V. Badanin, B.S. Pavlov, A.A. Pokrovski Acousto-optic scattering in a single-mode optic
fibre...................................27
A.S. Blagovestchenskii, A.A. Novitskaya\newline
On the solution of the wave equation asymptotically localized at infinity.......................................................................................................................................................................................34
A.V.Ivanov WKB-like method for the adiabatic limit of a pendulum type
equation...........................................................40
N.Ya.Kirpichnikova, V.B.Philippov, A.S.Kirpichnikova
Diffraction of electromagnetic waves from the impedance with different
perturbations.............................................................................................................................................................47
A.S. Kirpichnikova, V.B.Philippov
Diffraction by a line of jump of curvature (a special case).......................................60
A.V.Klimenko The Integral Equation Method for the Neumann-Kelvin Problem for an Interface-Intersecting Body in a Two-Layer Fluid
......................................................................................................................................................................70
P.V. Krauklis, L.A. Krauklis Unexpected wave in a cylindrical rod placed in the elastic
medium........................................
A.P. Krauklis, A.I. Malik, V.N.Troyan Direct and inverse problems of the ray tomography on the creeping
waves......86
A. Melezhik Polynomial Solutions of the Third-order Fuchsian Linear
ODE ....................................................................92
A.B. Mikhaylova, V.L.Oleinik Tight-binding investigation of the generalized Dirac
comb...............................................95
O.V. Motygin, P. McIver A uniqueness criterion for linear problems of wave-body
interaction.....................................108
M.V. Perel, I.V.Fialkovsky, A.P.Kiselev
An asymptotic theory of resonance interaction of shear and bending modes in a non-uniform Timoshenko
beam..........................................................................................................................................118
M.A.Poteryakhin Spectral series of the three-dimensional quantum anharmonic
oscillator..........................................127
A.Seeger Scattering by the Two-Dimensional Potential
sin f.........................................................................134
A.V.Shanin To the problem of diffraction on a slit: Some properties of Schwarzschild's
series......................................143
I. I Simonenko
On transient electromagnetic waves produced by the pulsed radial current moving with the velocity of
light.....................................................................................................................................................................................156
\S. Slavyanov, C. Ern, H. Dosch
Rigorous mathematical models for the reconstruction of thin films profiles from x-ray
intensities................................................................................................................................................................................161
S.Yu. Slavyanov
The equation for a product of solutions of two second-order linear ODEs.......................................168
E.A.Tropp, L.A.Bakaleinikov Addition theorem for Gegenbauer
functions....................................................................172
**