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