DAY on DIFFRACTION
PROCEEDINGS
June 1-3, 1999
St.Petersburg, Russia
Proceedings of the International Seminar ``Day on Diffraction99''
St.Petersburg , Russia June 1-3, 1999
edited by V.S.Buldyrev University of St.Petersburg
V.M.Babich St.Petersburg Branch of Mathematical Institute
I.V.Andronov University of St.Petersburg
V.E.Grikurov University of St.Petersburg
A.P.Kiselev Institute of Mechanical Engineering,
St.Petersburg
The seminar is sponsored by:
Russian Foundation for Basic Research
International Union of Radio Science
IEEE ED/MTT/AP St.Petersburg Chapter
(C) Day on Diffraction Faculty of Physics,
SPbU 1999
IEEE Catalog Number: 99EX367
ISBN 5-7997-0156-9
Print run 200
Reg. no 1058, Nov.11,1999
On
the 4th of July of 1999 the friends and the family celebrated the
70th anniversary of Professor Vladimir Sergeevitch Buldyrev
All his life
is closely bound with the faculty of physics of St.Petersburg State University.
He studied at this faculty as a student. Afterwards he worked there at
the Department of Mathematical Physics - first as an assistant professor,
later on as an associate professor, and finally as a professor. His wife
and both his sons also have graduated from the same faculty. Over thirty
students and over fifteen postgraduate students have been his direct pupils
and around ten of them are now professors at St.Petersburg State University
and at other universities.
The scientific
interests of Professor V.S. Buldyrev mainly lay in the field of mathematical
theory of diffraction. His first researches were devoted to analytic study
of explicit solutions for simple models. Further he turned to asymptotic
methods. Most problems for investigation were taken by him from important
physical applications. For studies in laser physics V.S. Buldyrev was awarded
the first Leningrad university Prize. For researches in geophysics he was
awarded the State Prize. Later he established important results in the
theory of acoustic waveguides. New researches of StPetersbourg school
in diffraction theory were presented in two monographs ``Short Wave Diffraction
Theory'' and ``Spacetime Ray Method'' with coauthorship of Prof. V.S.
Buldyrev. These monographs first were published in Russia and later were
translated into English. The third book ``Mathematical Methods in Modern
Electromagnetic Diffraction Theory'' is now in press in Japan. New style
in mathematical education realized by V.S. Buldyrev at the faculty of physics
is reflected in the textbook ``Functions of Many Variables and Linear Algebra''
written by V.S. Buldyrev in collaboration with B.S. Pavlov.
Professor
V.S. Buldyrev leads intensive organizing activity in his scientific field.
He was the Chairman of the local organizing Committee of URSI Symposium
on Electro magnetic Theory in 1995. Many years he is a CoChairman
of the annual workshop ''Day of Diffraction''.
Regular participants
of the workshop ''Day of Diffraction'' and former students of Prof. V.S.
Buldyrev congratulate him with the 70th anniversary and wish him health,
energy and scientific activity. On behalf of the Organizing Committee DD99
Professor Sergey Slavyanov
CONTENTS
Elena V. Aksenova, Vadim P. Romanov, Alexei Yu.
Val'kov
Green's Function of Electromagnetic Field in Cholesteric Liquid
Crystals with Largescale Periodicity ...................................................................
7 Victor V. Borisov
Formation of waves by a source distributed on a superluminal circle ...................................................................16
V.S. Buldyrev, T.V. Molokova Electromagnetic
waves propagation in a weakly chiral medium ............................................................................
21
L.A.Dmitrieva, D.A.Pyatkin
Spectral properties of polar operators with finitegap elliptic densities.................................................................26
Sergey V. Goldin, Anton A. Duchkov
Method of discontinuities and integral representation in the analysis
of wave field dynamics ................................................................................
32
Pavel Exner
Magnetoresonances in quantumdot resonators.....................................................................................................
40
E.Sh.Gutshabash
Darboux Transformation and Exact Solutions for the model of Cilindrically
Symmetrical Chiral field................ 48 Nakao
Hayashi, Hidetake Uchida, Pavel Naumkin
Analytic smoothing effect and global existence for elliptic hyperbolic
Davey Stewartson system ..........................................................................
57
A.Jodayree Akbarfam, E.Pourreza A research
note on the second order differential equation ................................................................................
65
Nakao Hayashi, Elena I. Kaikina
On the local and global existence of solutions to the nonlocal Whitham
equa tion on halfline .................................................................................77
V.B. Philippov, N.Ya. Kirpichnikova, A.S.
Kirpichnikova
Effects of diffraction of a creeping wave from a line of jump of
curvature .................................................................................................................
87
Yurii V. Kiselev, Vladimir N. Troyan
Restoration of Elastic and Velocity Parameters in Diffraction Tomography..............................................................................................................
97
Andrew V. Klimenko
The TwoDimensional NeumannKelvin Problem for an InterfaceIntersecting
Body in a TwoLayer Fluid.......103
P.V.Krauklis, A.P.Krauklis
New guided wave in a poroacoustic layer ................................................................................................................113
P.V.Krauklis, L.A.Krauklis
Slow wave diffraction at a borehole ..........................................................................................................................117
L.A. Dmitrieva, D.D. Gushin, Yu.A. Kuperin
Generalized spectral analysis of some exactly solvable chaotic maps.......................................................................................................................122
I.V. Lindell, L.H. Ruotanen, F. Olyslager
Electromagnetic Field and Source Decomposition in a Class of Linear
Media ........................................................................................................129
Oleg V. Motygin, Andrew V. Klimenko
On NonUniqueness in the 2D Linear Problem of a TwoLayer
Flow about InterfacePiercing Bodies ..................................................................137
Nakao Hayashi, Pavel Naumkin
On the modified Korteweg de Vries equation .........................................................................................146
Igor E.Ogorodnikov
The asymptotic behaviour for large values of the time of energy of boundary
value problem with mixed boundary conditions for Rossby wave equation........................................................................................................................................................
157
M.Boiti, F.Pempinelli, B. Prinari, A.K.Pogrebkov
Nwave soliton solution on a generic background for KPI equation.........................................................................................................................
167
Andrey V. Shanin
An Extension of WienerHopf Method: Ordinary Differential Equations
Asso ciated with Diffraction Problems ..... 176
I.I. Simonenko
Formation and destruction of waves with singularities on the spherical
wave front ......................................................183
S.Yu.Slavyanov
Multipole matrix elements ................................................................................................................................................
189
Vladislav V. Yatsenko, Stanislav I. Maslovski
Electromagnetic diffraction by double arrays of dipole scatterers..............................
196
A. V. Kudrin, E. Yu. Petrov, T. M. Zaboronkova
Current behavior on a perfectly conducting cylinder with a deltagap
excitation in an anisotropic medium ..........................................................
210
Alexei V. Popov, Ning Yan Zhu
Curved Oversized EM Waveguides: Adiabatic Modes and Parabolic Equation
..................................220