Moscow State University, Department of Physics, Acoustics Division
Andrey V. Shanin
you can write me: a.v.shanin (round letter "a" with a tail) gmail (I am tired of spam) com
tel: +7(095) 9393081
address: 119992, Moscow, Leninskie Gory, Moscow State University, Department of Physics
Education
 1988  Moscow 57th high school
 1994  M.Sc. Department of Physics, Moscow State University
 1997  Ph.D. Department of Physics, Moscow State University
Professional positions
 19972000: Researcher, Department of Physics, Moscow State University
 20002003: Senior researcher, Department of Physics, Moscow State University
 2003present: Reader, Department of Physics, Moscow State University
Research interests
Elastic wedges and functional equations
 A.V.Shanin, On wave excitation in a wedgeshaped region
// Acoustical Physics, 1996, 42, 5, 612617.
 A.V.Shanin, Excitation and scattering of a wedge wave
in an obtuse elastic wedge close to 180 // Acoustical
Physics, 1997, V. 43, N.3, pp. 344349.
(djvu, Russian)
 A.V.Shanin, Excitation of waves in a wedgeshaped region //
Acoustical Physics, 1988, V.44. N.5, pp.592597
(scanned PDF file, English version)
 A.V.Shanin, Excitation of wave field in a triangle area //
Int. sem. "Days on Diffraction 97",
proceedings pp. 205210,
1997, june 35, S.Pb.
 A.V.Shanin, Excitation of wave field in a triangular area with impedance boundary
Zapiski seminarov POMI, 1988, V.250, pp.300318 (in Russian)
(PDF file, English version)
 A.V.Shanin, V.V.Krylov, An approximate theory for waves in a thin
elastic wedge immersed in liquid // Proc.Roy.Soc.L.A, V. 456, N 2001,
21792196 (2000) (PDF file)
Embedding formulae

A.V.Shanin, Embedding formula for electromagnetic diffraction problem //
Zapiski seminarov POMI, V.324, pp.247261 (2001), in Russian,
(PDF file, Russian version)
(PDF file, English version)
 R.V.Craster, A.V.Shanin, Embedding formulae for planar cracks
// Advanced research workshop "Surface waves in anisotropic and
laminated bodies and defect detection", 79 February 2002, Moscow
 A.V.Shanin, R.V.Craster, Removable singular points for ordinary
differential equations //
Europ.
J. Appl. Math V.13. N 6. pp. 617639 (2002).
(PDF file)
(CUP)
 R.V.Craster, A.V. Shanin, E.M.Doubravsky, Embedding formulae in diffraction theory
// Proc.Roy.Soc.Lond.A (2003) V.459, 24752496.
(PDF file)
 R.V.Craster, A.V.Shanin, Embedding formula for diffraction by wedge and angular geometries
// PRSLA, (2005) V.461, 22272242 (PDF file)
 E.A.Skelton, R.V.Craster, A.V.Shanin, Embedding formulae for diffraction by nonparallel
slits // Quart. Journ. Mech. Appl.Math. V. 61. N.1, pp 93116 (2008).
(manuscript, PDF file)
 A.V.Shanin, R.V.Craster, Pseudodifferential operators for embedding formulae //
Journ. Comp. Appl. Math. V.234, pp. 16371646 (2010)
(manuscript, PDF file)
 E.A. Skelton, R.V. Craster, A.V. Shanin, V.Valyaev. Embedding formulae for scattering by
threedimensional structures. Wave Motion, Vol. 47 (2010) pp. 299–317.
(manuscript, PDF file) doi:10.1016/j.wavemoti.2009.11.006
2D diffraction problems (strips etc),
generalization of the WienerHopf method, spectral equation method, coordinate equations
 A.V.Shanin, An extension of WienerHoph method:
Ordinary differential equations associated with diffraction problems //
Proceedings of the Int. Sem. "Days on Diffraction
99", 1999, June 13, S.Pb., pp 176182.
(PDF file)
 A.V.Shanin, Three theorems concerning diffraction by a strip or a slit // Q.Jl Mech.
Appl. Math. V. 54, No 1, pp. 107137 (2001) (manuscript, PDF file)
 A.V.Shanin, S.V.Chernyshev, Diffraction by two ideal strips //
Int. Sem. "Days on Diffraction 2001",
May 2931(2001), S.Pb. (PDF file)
 A.V.Shanin, Diffraction of a plane wave by two ideal strips //
Q.Jl Mech. Appl. Math. V. 56, No 2, pp. 187215 (2001)
(manuscript, PDF file)
 A.V.Shanin, To the problem of diffraction on a slit. Some properties of Schwarzschild's series //
Zapiski seminarov POMI, V.275, ñ.258285 (2001), in Russian,
(PDF file, Russian version)
(PDF file, English version)
 A.V.Shanin, On the connection between the Wienerhopf method
and the theory of ordinary differential equations // Electromagnetic waves and electronic systems
2002, V.7, N 7. (PDF file, English version)
 A.V.Shanin, Further progress in the coordinate equations theory //
Int. Sem. "Days on Diffraction
2002", 2002, June 58, S.Pb. (PDF file)
 A.V.Shanin, A generalization of the separation of variables method for
some 2D diffraction problems // Wave Motion, V.37, N.3, pp. 241256 (2003)
(manuscript, PDF) doi:10.1016/S01652125(02)00077X
 A.V.Shanin, Diffraction by a flat cone //
Int. Sem. "Days on Diffraction
2003", 2003, June 2227, S.Pb. (PDF file)
 A.V.Shanin, E.M.Doubravsky. Acoustical scattering at a gap between two orthogonal,
semiinfinite barriers: coordinate and spectral equations //
Journ. Eng. Math., V. 59, N.4, 2007, pp.437449.
(manuscript, PDF file)
 Shanin A.V., Edge Green’s functions on a branched surface. Asymptotics of solutions of coordinate and
spectral equations // Journal of Mathematical Sciences,
V. 148, N5, pp. 769783 (2008).
 Shanin A.V. Edge Green's functions on a branched surface.
Statement of the problem of finding unknown constants//
V. 155, N3, pp. 461474 (2008).
 A.V. Shanin, V.Yu. Valyaev. Numerical procedure for solving the strip problem by the spectral equation
// Journal of Computational Acoustics. V. 19, No 3, P. 269290 (2011).
 A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip I. Reducing diffraction problem to RiemannHilbert problems, QJMAM, 68, PP. 321339, 2015, arXiv preprint
 A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip II. Solving Riemann–Hilbert problems by OE–equation method, QJMAM, 68, PP. 341362, 2015,
arXiv preprint
Research on conical problems
 Shanin A.V., Diffraction by a flat cone //
Int. Sem. "Days on Diffraction
2003", 2003, June 2227, S.Pb. (PDF file)
 Shanin A.V., Modified Smyshlyaev's formulae for the problem of diffraction of a plane wave by an ideal quarterplane //
Wave Motion, V.41, N1, pp. 7993.
doi:10.1016/j.wavemoti.2004.05.005
 Shanin A.V., Coordinate equations for the LaplaceBeltrami problem on a sphere with a cut // QJMAM, 2005 (58) 2, 120
The preprint versions of two previous papers have been sent to URSI contest: Paper 1, PDF file,
Paper 2, PDF file. Failed. Sad but true.
 Valyaev V.Yu, Shanin A.V. Derivation of modifed Smyshlyaev's formulae using
integral transform of KontorovichLebedev type // Int. Sem. "Days on Diffraction
2010", 2010, June 2227, S.Pb. (PDF file)
 A.V. Shanin, Diffraction series on a sphere and conical asymptotics //
Proceedings of Days on Diffraction'2011, June 2010, S.Pb. PDF file
 A.V.Shanin, Asymptotics of waves diffracted by a cone and diffraction series on a sphere // Zapiski Nauch Sem POMI
RAN V.393, P. 234258, 2011 PDF in Russian
, English translation
 V.Valyaev, A.V.Shanin. Embedding formulae for LaplaceBeltrami problems on the sphere with a cut
// Wave Motion 2012, V.49, N1, pp. 8392. doi:10.1016/j.wavemoti.2011.07.004
manuscript, PDF
Embedding formula and spectral equation for Weinstein's class diffraction gratings. Processes in waveguides near the cutoff frequencies
 Shanin A.V. Weinstein's diffraction problem: embedding formula and
spectral equation in parabolic approximation // SIAM Journ. Appl. Math. V.70. N4, pp.12011218
(2009) (PDF file)
 Shanin A.V. Diffraction of a highfrequency grazing wave by a grating with a complicated period
(English translation of a paper published in Zap. nauch. sem. POMI RAN, 2012, 409, to appear in Journal of
Mathematical Sciences) (PDF file)
 S.A.Nazarov, A.V. Shanin, Trapped modes in angular joints of 2D waveguides // Applicable Analysis. V.93, N 3 (2014) 572582.
 A.I.Korolkov, A.V.Shanin, Diffraction by a grating consisting of absorbing screens of different height.
New equations // Zap. Nauch. Sem. POMI, V. 422, P. 6289 (2014),
to be translated in J.Math.Sci. (PDF file)
 A.V.Shanin, A.I.Korolkov, Wave Reflection from a Diffraction Grating Consisting of Absorbing
Screens: Description in Terms of the Wiener–Hopf–Fock Method // Acoust. Phys., V.60, N.5, P.624632. (2014)
(PDF file)
Waveguides and resonators
 O.V.Rudenko, A.V.Shanin, Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by
finite displacement of its boundary // Acoustical physics, V.46, No.3, pp.334341 (2000).
 A.V. Shanin, M.S. Dorofeev, Wave modes in periodic systems of thin tubes, Proceedings of International conference
“Days on Diffraction 08”, S.Pb, June 36, pp.163168. (PDF file)
 Dorofeev M.S., Shanin A.V. Resonances in a discrete system of variable
length // Acoustical Physics V. 55, N 3, pp 307314 (2009)
 E. D. Shabalina, N. V. Shirgina, and A. V. Shanin. High Frequency Modes
in a Two Dimensional Rectangular Room with Windows // Acoustical Physics, (2010), Vol. 56, No. 4, pp. 525–536.
 S.A. Nazarov, A.V. Shanin,
Trapped modes in angular joints of 2D waveguides,
Applicable Analysis, 93, PP. 572582, 2014.
 A.I.Korolkov, S.A.Nazarov, A.V.Shanin,
Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves,
ZAMM, 96, PP. 12451260, 2016.
 A.V.Shanin, A.I.Korolkov,
Diffraction of a mode close to its cutoff by a transversal screen in a planar waveguide,
Wave Motion, 68, PP. 218241, 2017.
 A.V.Shanin,
Precursor wave in a layered waveguide,
JASA, 141, PP. 346356, 2017. arXiv preprint
 K.S.Knyazeva, A.V.Shanin
Transient phenomena in a threelayer waveguide and the analytical structure of the dispersion diagram,
Submitted to Wave Motion,
arXiv preprint
Integral equation formalism for the parabolic equation of diffraction theory
 A.I.Korolkov, A.V.Shanin,
The parabolic equation method and the Fresnel approximation in the application to Weinstein's problems,
Journal of Mathematical Sciences, 214, PP. 302321, 2016.
 A.V.Shanin, A.I.Korolkov,
Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation,
Submitted to SIAM J.Appl.Math., arXiv preprint
Research on matrix factorization

A.V.Shanin, E.M.Doubravsky, Criteria for commutative factorization of a class of algebraic matrices
arXiv preprint

A.V.Shanin, An ODEbased approach to some RiemannHilbert problems motivated by wave diffraction
arXiv preprint

A.V.Shanin, WienerHopf matrix factorization using ordinary differential equations in the commutative case
arXiv preprint
Published as
A.V.Shanin, Solution of RiemannHilbert problem related to WienerHopf factorization problem using ordinary
differential equations in the commutative case // Quart. Journ. Mech. Appl. Math. Vol. 66, No 4, pp. 533555 (2013) doi:10.1093/qjmam/hbt017.
D.Sci. thesis (the defence took place on November 18, 2010)
It is entitled "New differential equations for the canonical diffraction problems" (PDF file, in Russian)
The abstract (30 pages) is here, in Russian also
Note
The right of distribution of each paper belongs to the publisher of corresponding Journal. However,
usually I retain the right to post here a preprint or the final version of the paper, for educational
purposes only. So if you want to use these materials for something else than education, please
visit a library or the journal site.