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
Application of multivariable complex analysis
 R.C.Assier, A.V.Shanin, Analytical continuation of twodimensional wave fields //
To appear in RSPA (2021)
arXiv:2008.10673
 R.C.Assier, A.V.Shanin, Diffraction by a quarter–plane. Analytical continuation of spectral functions //
QJMAM, V.72, N.1, P.5185 (2019)
(Open access)
 R.C.Assier, A.V.Shanin, Towards a multivariable WienerHopf method,
A minicourse in Isaac Newton Institute (Cambridge),
Seminar "Bringing pure and applied analysis together via WienerHopf Technique"
Lecture 1 ,
Lecture 2 ,
Lecture 3 ,
Lecture 4 ,
Lecture 5
Lattices. Analytical approach and numerical techniques

A.V.Shanin, A.I.Korolkov,
Diffraction by a Dirichlet right angle on a discrete planar lattice //
Submitted to Wave Motion
arXiv preprint

A.V.Shanin, A.I.Korolkov,
Sommerfeldtype integrals for discrete diffraction problems //
Wave Motion, V.97, 102606 (2020) DOI:10.1016/j.wavemoti.2020.102606
arXiv preprint

J.PobletPuig, A.V.Shanin,
A New Numerical Method for Solving the Acoustic Radiation Problem //
Acoustical Physics, V.64, N.2, P.252259 (2018)
arXiv preprint

J.PobletPuig, A.V.Shanin,
A boundary algebraic formulation for plane strain elastodynamic scattering //
SIAM Journal on Applied Mathematics, V.78, N.2, P.12561282 (2018)

J.PobletPuig, V.Yu.Valyaev, A.V.Shanin,
Suppression of spurious frequencies in scattering problems by means of boundary algebraic and combined field equations //
J. Int. Eq. Appl., V.27, N.2, P.233272 (2015)

J.PobletPuig, V.Yu.Valyaev, A.V.Shanin,
Boundary element method based on preliminary discretization
â æóðíàëå Mathematical Models and Computer Simulations, V.6, N.2, P.172182. (2014)
Waveguides and resonators
 M.A.Mironov, A.V.Shanin, A.I.Korolkov, K.S.Kniazeva,
Exchange pulse related to phase synchronism in gasplate structure // Submitted to Journ. Sound Vibr.
arXiv preprint
 A.V.Shanin, K.S.Knyazeva, A.I.Korolkov
Riemann surface of dispersion diagram of a multilayer acoustical waveguide
Wave Motion, V.83. P.148172. DOI: 10.1016/j.wavemoti.2018.09.010
arXiv preprint
 A.V.Shanin,
Precursor wave in a layered waveguide,
JASA, 141, PP. 346356, 2017. arXiv preprint
 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.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.
 S.A. Nazarov, A.V. Shanin,
Trapped modes in angular joints of 2D waveguides,
Applicable Analysis, 93, PP. 572582, 2014.
 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.
 Dorofeev M.S., Shanin A.V. Resonances in a discrete system of variable
length // Acoustical Physics V. 55, N 3, pp 307314 (2009)
 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)
 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).
2D diffraction problems (strips etc),
generalization of the WienerHopf method, spectral equation method, coordinate equations
 R.C.Assier, A.V.Shanin, Analytical continuation of twodimensional wave fields //
To appear in RSPA (2021)
arXiv:2008.10673
 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
 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, 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).
 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).
 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).
 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)
 A.V.Shanin, Diffraction by a flat cone //
Int. Sem. "Days on Diffraction
2003", 2003, June 2227, 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, 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, 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, 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, S.V.Chernyshev, Diffraction by two ideal strips //
Int. Sem. "Days on Diffraction 2001",
May 2931(2001), S.Pb. (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, 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)
Research on conical problems
 R.C.Assier, A.V.Shanin, Diffraction by a quarter–plane. Analytical continuation of spectral functions //
QJMAM, V.72, N.1, P.5185 (2019)
(Open access)
 V.Yu.Valyaev, A.V.Shanin, Measurement of the Diffraction Coefficient of a Trihedral Cone with Homogeneous Neumann Boundary Conditions // PIERS Proceedings, Toyama 2018, DOI:10.23919/PIERS.2018.8597926
 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
 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
 A.V. Shanin, Diffraction series on a sphere and conical asymptotics //
Proceedings of Days on Diffraction'2011, June 2010, S.Pb. PDF file
 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)
 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.
 Shanin A.V., Modified Smyshlyaev's formulae for the problem of diffraction of a plane wave by an ideal quarter plane //
Wave Motion, V.41, N1, pp. 7993. doi:10.1016/j.wavemoti.2004.05.005
 Shanin A.V., Diffraction by a flat cone //
Int. Sem. "Days on Diffraction
2003", 2003, June 2227, S.Pb. (PDF file)
Embedding formula and spectral equation for Weinstein's class diffraction gratings. Processes in waveguides near the cutoff frequencies
 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)
 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)
 S.A.Nazarov, A.V. Shanin, Trapped modes in angular joints of 2D waveguides // Applicable Analysis. V.93, N 3 (2014) 572582.
 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)
 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)
Integral equation formalism for the parabolic equation of diffraction theory
 A.I.Korolkov, A.V.Shanin, A.A.Belous, Diffraction by an Elongated Body of Revolution with Impedance Boundaries: the Boundary Integral Parabolic Equation Method // Acoustical Physics, V.65, N.4, P.340347
 A.V.Shanin, A.I.Korolkov,
Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation,
Wave Motion, V. 85, N.1, P.176190. DOI: 10.1016/j.wavemoti.2018.10.006
arXiv preprint
 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.I.Korolkov, A.V.Shanin,
Highfrequency diffraction by an impedance segment at oblique incidence // Acoustical phyiscs, V. 62, No. 6, PP. 651658 (2016)
 A.I.Korolkov, A.V.Shanin,
Highfrequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach
// Acoustical Physics, V.62, N.4, P.405413
Research on matrix factorization

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.

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

A.V.Shanin, E.M.Doubravsky, Criteria for commutative factorization of a class of algebraic matrices
arXiv preprint
Embedding formulae
 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
 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, Embedding formulae for diffraction by nonparallel
slits // Quart. Journ. Mech. Appl.Math. V. 61. N.1, pp 93116 (2008).
(manuscript, PDF file)
 R.V.Craster, A.V.Shanin, Embedding formula for diffraction by wedge and angular geometries
// PRSLA, (2005) V.461, 22272242 (PDF file)
 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 formulae for planar cracks
// Advanced research workshop "Surface waves in anisotropic and
laminated bodies and defect detection", 79 February 2002, Moscow

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)
Elastic wedges and functional equations
 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)
 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, 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 waves in a wedgeshaped region //
Acoustical Physics, 1988, V.44. N.5, pp.592597
(scanned PDF file, English version)
 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, On wave excitation in a wedgeshaped region
// Acoustical Physics, 1996, 42, 5, 612617.
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.