Aleksei P. Kiselev



Given name:


Patronymic name:


Contact info:

Tel: + 7 (812) 321-47-66

Fax: + 7 (812) 321-47-71

E-mail: aleksei.kiselev at

Address: V.O., Bolshoy pr., 61, St. Peters­burg, 199178, Russia, IPME RAS

Home page: RU EN

Position in IPME RAS:

Principal Research Scientist

Laboratory for Mathematical Modelling of Wave Phenomena

Academic degree:

Ph. D., D. Sc.



Дата рождения:


Professional activity:

1965–1971 — Leningrad State University, student

1971–1977 — Steklov Mathematical Institute Leningrad Branch, researcher, engineer

1977–1988 — Rudgeofizika Corporation, engineer, senior researcher

since 1988 — IPME RAS, researcher, senior researcher, principal research Scientist (part-time since 2002)

since 2002 — Steklov Institute St. Peters­burg Department, Principal Research Scientist

Scientific interests:

  • Diffraction and propagation

  • Linear theory of elastic waves

  • Localized waves in optics and acoustics


St. Peters­burg Mathematical Society

Dissertation councils:

Steklov Institute St. Peters­burg Department (Mathematical Physics)

Editorial boards:

Proceedings of the Conference Days on Diffraction


St. Peters­burg State University, Department of Higher Mathematics and Mathematical Physics, Professor

Organizing conferences:

Annual International Conference Days on Diffraction

Profiles in scientific databases and networks:

Google Scholar





  • Kiselev A.P. High-frequency point sources in inhomogeneous elastic medium, Sov. Phys. Doklady 19(4), 855–856, 1974.

  • Kiselev A.P. High-frequency source between the branches of a hyperbola, J. Math. Sci. 3(1), 62–81, 1975.

  • Arkhipov V.M., Bytsenko A.A., Parshin P.F., Kiselev A.P. Common periodic interference modulation properties in a Fourier spectrometer and a spectrometer with interference selective amplitude modulation, J. Appl. Spectr. (translation of Zh. Prikl. Spektrosk.) 24(5), 878–885, 1976.

  • Kiselev A.P. Diffraction by a wedge with a circular cap, J. Appl. Math. Mech. (translation of PMM) 24(5), 981–984, 1977.

  • Kiselev, A.P. Focusing of WKB solutions of the equation [∆+k2n2(x)]u=0, k→∞, J. Math. Sci. 11(3), 444–448 (1979).

  • Kiselev A.P. Electromagnetic field in a neighborhood of a focus, J. Math. Sci. 11(5), 744–752, 1979.

  • Kiselev A.P. The general solution of the equations of elasticity theory, Sov. Tech. Phys. Lett. 6(8), 391–392, 1980.

  • Kiselev A.P. Focal boundary layer in axisymmetric diffraction problems, Radiophys. & Quant. Electron. 23(3), 241–252, 1980.

  • Kiselev A.P. Edge waves, Sov. Tech. Phys. Lett. 7(3), 119–120, 1981.

  • Kiselev A.P. Excitation of modulated oscillations in inhomogeneous media, J. Math. Sci. 20(1), 1118–1125, 1982.

  • Kiselev A.P. Small spherical emitter in an inhomogeneous elastic medium, Mech. Solids (translation of Izv. Acad. Sci. USSR. MTT.) 17(4), 106–114, 1982.

  • Kiselev A.P., Frolova E.N. Transverse wave from a nondirectional source in an inhomogeneous elastic medium, Izv. Acad. Sci. USSR. Phys. Solid Earth 18(5), 323–328, 1983.

  • Kiselev A.P. Energy balance equations describing point sources of elastic waves in a continuously varying medium, Sov. Phys. – Tech. Phys. 28(2), 131–139, 1983.

  • Kiselev A.P. Modulated Gaussian beams, Radiophys. & Quant. Electron. 26(8), 755–761, 1983.

  • Kiselev A.P. Extrinsic components of elastic waves, Izv. Acad. Sci. USSR. Phys. Solid Earth 19(5), 707–710, 1984.

  • Kiselev A.P. Propagation of Gaussian beams along the edge of the wedge, Sov. Tech. Phys. Lett. 10(11), 581–582, 1984.

  • Kiselev A.P. Slender cylindrical emitter in an inhomogeneous elastic medium, Sov. Phys. – Tech. Phys. 29(2), 209–215, 1984. Erratum: 31(1), 135, 1986.

  • Grikurov V.E., Kiselev A.P. Gaussian beams at large distances, Radiophys. & Quant. Electron. 29(3), 233–237, 1986.

  • Gavrilov A.V., Kiselev A.P. Influence of media inhomogeneity and the source pattern on the polarization of elastic P-waves, Izv. Acad. Sci. USSR. Phys. Solid Earth 22(6), 494–496, 1986.

  • Kiselev A.P. Depolarization in diffraction, Sov. Phys. – Tech. Phys. 32(6), 695–696, 1987.

  • Kiselev A.P. Point sources of vibrations in a weakly anisotropic elastic media, Sov. Phys. Doklady 33(6), 466–467, 1988.

  • Babich V.M., Kiselev A.P. Ray description of the ‘nongeometrical’ S* wave, Izv. Acad. Sci. USSR. Phys. Solid Earth 24(10), 817–820, 1988.

  • Kiselev A.P., Tsvankin I.D. A method of comparison of exact and asymptotic wave field computations, Geophys. J. 96(2), 253–258, 1989.

  • Babich V.M., Kiselev A.P. Non-geometrical waves – are there any? An asymptotic description of some ‘nongeometrical’ phenomena in seismic wav propagation, Geophys. J. Int. 99(2), 412–420, 1989.

  • Kirpichnikova N.Ya., Kiselev A.P. Depolarization of elastic surface waves in a vertically inhomogeneous half-space, Sov. Phys. Acoustics 36(1), 173–175, 1990.

  • Kirpichnikova N.Ya., Kiselev A.P. Polarization spectral anomalies of surface waves in an almost layered elastic halfspace, J. Math. Sci. 50(6), 2001–2011, 1990.

  • Kiselev A.P., Roslov Yu.V. Use of additional components for numerical modelling of polarization anomalies of elastic body waves, Sov. Geology & Geophysics 32(4), 105–114, 1991.

  • Kiselev A.P. Higher-order terms of the ray theory and ‘non-geometrical phenomena’ in inhomogeneous viscoelastic media, Izvestia Russ. Acad. Sci., Phys. Solid Earth 28(11), 946–948, 1992.

  • Kiselev A.P. Ray theory of modulated body waves in an inhomogeneous viscoelastic medium, Pure Appl. Geophysics 140(4), 629–640, 1993.

  • Kiselev A.P. Body waves in a weakly anisotropic medium. – I. Plane waves, Geophys. J. Int. 118(1), 383–400, 1994.

  • Kirpichnikova N.Ya., Kiselev A.P. On the anomalous polarization of Love and Rayleigh elastic waves in layered medium, J. Math. Sci. 73(3), 383–384, 1995.

  • Kiselev A.P., Yarovoy V.O. Diffraction, interference and depolarization of elastic waves. – I. Polarization anomalies near a low-contrast interface, Izvestia Russ. Acad. Sci., Phys. Solid Earth 30(11), 960–966, 1995.

  • Fradkin L.Ju., Kiselev A.P. The two-component representations of time-harmonic elastic body waves at high- and intermediate-frequency regimes, J. Acoust. Soc. Amer. 101(1), 52–65, 1997.

  • Kiselev A.P., Lazarev V.A. Bouncing of the load and radiation of sound in dry friction, Tech. Phys. 42(5), 581–583, 1997.

  • Kiselev A.P., Krylova E., Fradkin L.Yu. Excitation of a quasi-plane shear wave by a surface acoustic source producing normal stresses, Tech. Phys. Lett. 23(12), 941–942, 1997.

  • Kiselev A.P., Rogoff Z.M. Diffraction at a jump of curvature on an impedance boundary, Day on Diffraction '97, Proceedings, St. Peters­burg University Press, 59–65, 1997.

  • Kiselev A.P., Perel M.V. Quasiphotons and nondispersive waves, Day on Diffraction '97, Proceedings, St. Peters­burg University, 86–90, 1997.

  • Fradkin L.Ju., Kiselev A.P., Krylova E. The radiating near-field asymptotics of a normal time-harmonic circular ultrasonic transducer in an elastic half-space, J. Acoust. Soc. Amer. 104(3), pt 1, 1178–1187, 1998.

  • Fradkin L., Kiselev A., Gridin D., Krylova E. Radiating near-field of a compressional circular ultrasonic transducer, Non-Destructive Testing. An Eastern – Western European Perspective. Ed. B. Bridge, A. Khalid, B. Yochev. British Institute of Nondestructive Testing, 129–152, 1998.

  • Kiselev A.P., Rogoff Z.M. Dilatation of S-waves in smoothly inhomogeneous isotropic elastic media, J. Acoust. Soc. Amer. 104(5), 2592–2495, 1998.

  • Aref'ev A.V., Kiselev A.P. Viscoelastic Rayleigh waves in a layered structure with weak lateral inhomogeneity, J. Math. Sci. 91(2), 2701–2705, 1998.

  • Aref'ev A.V., Kiselev A.P. Viscoelastic Love waves in a layered structure with weak lateral inhomogeneity, J. Math. Sci. 96(4), 3289–3291, 1999.

  • Kiselev A.P., Perel M.V. On the nature of ‘quasiphotons’, J. Math. Sci. 96(4), 3355–3358, 1999.

  • Kiselev A.P. Nondispersive edge modes, Wave Motion 29(2), 111–117, 1999.

  • Kiselev A.P., Perel M.V. Gaussian wave packets, Optics & Spectroscopy 86(3), 357–359, 1999.

  • Kiselev A.P., Perel M.V. Highly localised solutions of the wave equation, J. Math. Phys. 41(4), 1934–1955, 2000.

  • Borisov V.V., Kiselev A.P. A new class of relatively undistorted progressing waves, Appl. Math. Lett. 13(4) 83–86, 2000.

  • Lindell I.V., Kiselev A.P. Polyadic methods in elastodynamics, Progress in Electromagnetics Research 31, 113–154, 2000.

  • Perel M.V., Fialkovsky I.V., Kiselev A.P. An asymptotic theory of resonance interaction of shear and bending modes in a nonuniform Timoshenko beam, Day on Diffraction'00, Proceedings, St. Peters­burg University Press, 118–126, 2000.

  • Rogoff Z.M., Kiselev A.P. Diffraction at jump of curvature on an impedance boundary, Wave Motion 33(2), 225–243, 2001.

  • Babich V. M., Kiselev A.P., Lawry J.M.H., Starkov A.S. A ray description of all waves generated by a high-frequency point source near an interface, SIAM J. Appl. Math. 62(1), 21–40, 2001.

  • Kiselev A.P. Body waves in a weakly anisotropic medium. – II. S wave from a centre of expansion and P wave from a centre of rotation, Geophys. J. Int. 145(3), 714–720, 2001.

  • Kiselev A.P., Vsemirnova E.A., Dyakova G.N. Dilatation of S waves and rotation of P waves in weakly anisotropic elastic media, Days on Diffraction '01, St. Peters­burg University Press, 140–143, 2001.

  • Kiselev A.P., Klimova A.A. A plane shear wave excited in an elastic half-space by oscillating normal pressure distributed nonuniformly. J. Math. Sci. 108(5), 703–709, 2002. Erratum: 117(2), 3947, 2003.

  • Kiselev A.P., Perel M.V. Relatively undistorted progressive waves for the m-dimensional wave equation, Differential Equations 38(8), 1128–1129, 2002.

  • Buldyrev V.S., Vershik A.M., Ibragimov I.A., Il'in A.M., Kiselev A.P., Faddeev L.D. Vasilii Mikhailovich Babich (on his 70th birthday), Russ. Math. Surveys 57(3), 181–187, 2002.

  • Kiselev A.P., Starkov A.S. Parabolic equation and Pearcey-type integral for a transmitted wave field, J. Math. Sci. 117(2), 3945–3946, 2003.

  • Perel M.V., Fialkovsky I.V., Kiselev A.P. Resonance interaction of bending and shear modes in a non-uniform Timoshenko beam, J. Math. Sci. 111(5), 3775–3790, 2002.

  • Kiselev A.P. Relatively undistorted progressive waves. New examples, J. Math. Sci. 117(2), 3945–3946, 2003.

  • Kiselev A.P., Smyshlyaev V.P. The 70-th birthday of V. M. Babich, J. Math. Sci. 117(2), 3891–3894, 2003.

  • Kiselev A.P. A new attenuation factor for the Bateman nondispersive wave solution, J. Electromagnetic Waves and Applications 17(1), 115–120, 2003.

  • Kiselev A.P. Generalisation of Bateman–Hillion progressive wave and Bessel–Gauss pulses solutions of the wave equation via a separation of variables, Journal of Physics A: Math. Gen. 36(23), L345–L349, 2003.

  • Kiselev A.P. New structures in paraxial Gaussian beams, Optics & Spectroscopy 96(4), 533–535, 2004.

  • Kiselev A.P. Rayleigh wave with a transverse structure, Proc. Roy. Soc. London A 460(2050), 3059–3064, 2004.

  • Babich V.M., Kiselev A.P. “Nongeometrical phenomena” in propagation of elastic surface waves, Surface Waves in Anisotropic and Laminated Bodies and Defects Detection. Proceedings of the NATO Advanced Workshop, ed. R. V. Goldstein and G. A.Maugin, Kluwer, 119–129, 2004.

  • Volyar A.V., Kiselev A.P., Egorov Yu.A. Eigen-polarization beams in uniaxial crystals, Proc. SPIE, 5582, 98–105, 2004.

  • Kiselev A.P., Yarovoy V.O., Vsemirnova E.A. Polarization anomalies of elastic waves. Caustic and Penumbra, J. Math. Sci. 127(6), 2413–2423, 2005.

  • Bécache E., Kiselev A.P. Non-stationary elastic wavefields from an apodized normal transducer. Near-field asymptotics and numerics, Acta Acustica united with Acoustica 91(5), 822–830, 2005.

  • Kiselev A.P. Relatively undistorted cylindrical waves depending on three spatial variables, Math. Notes 79(4), 635–636, 2006.

  • Kiselev A.P., Huet G., Deschamps M. Waveforms in additional components of elastic bulk waves, J. Math. Sci. 142(6), 2571–2575, 2007.

  • Kiselev A.P. Localized light waves: Paraxial and exact solutions of the wave equation (a review), Optics & Spectroscopy 102(4), 603–622, 2007.

  • Kiselev A.P., Ducasse E., Deschamps M., Darinskii A. Novel exact surface wave solutions for layered structures, Comptes Rendus Mécanique 335(8), 419–422, 2007.

  • Shuvalov A.L., Poncelet O., Kiselev A.P. Shear horizontal waves in transversely inhomogeneous plates, Wave Motion 45(5), 605–615, 2008.

  • Kiselev A.P. Plane waves with a ransverse structure in arbitrarily anisoptropic elastic medium, Doklady Physics 53(1), 48–50, 2008.

  • Kiselev A.P., Tagirdzhanov A.M. Love waves with a transverse structure, Vestnik St. Peters­burg University. Mathematics 41(3), 278–281, 2008.

  • Tagirdzhanov A.M., Blagovestchenskii A.S., Kiselev A.P. “Complex Source” in real space, Progress in Electromagnetics Research Symposium, Moscow 2009, 1527–1529, 2009.

  • Kamotskii I.V., Kiselev A.P. An energy approach to the proof of the existence of Rayleigh waves in an anisotropic elastic half-space, J. Appl. Math. Mech. 73(4), 464–470, 2009.

  • Parker D.F., Kiselev A.P. Rayleigh waves having generalized lateral dependence, Quart. J. Mech. Appl. Math. 62(1), 19–29 (2009).

  • Kiselev A.P., Rogerson G.A. Laterally dependent surface waves in an elastic medium with a general depth dependence, Wave Motion 46(8), 539–547, 2009.

  • Kiselev A.P., Parker D.F. Omni-directional Rayleigh, Stoneley and Schölte waves with general time- dependence, Proc. Royal Society London A 466(2120), 3059–3064, 2010.

  • Babich V.M., Kiselev A.P. “Days on Diffraction”, successor of all-USSR symposia and schools on diffraction theory, J. Math. Sci. 175(6), 621–622, 2011.

  • Ibragimov I.A., Il'in A.M., Kiselev A.P., Kislyakov S.V., Faddeev L.D. Vasilii Mikhailovich Babich (on his eightieth birthday), Russ. Math. Surveys 66(1), 205–207, 2011.

  • Tagirdzhanov A.M., Blagovestchenskii A.S., Kiselev A.P. “Complex source'” wavefields: sources in real space, J. Phys. A: Math. Theor. 44(42) pap. 425203, 2011.

  • Kiselev A.P., Plachenov A.B. Exact solutions of the m-dimensional wave equation from paraxial ones. Further generalizations of the Bateman solution, J. Math. Sci. 185(4), 605–610, 2012.

  • Kiselev A.P., Plachenov A.B., Chamorro-Posada P. Nonparaxial wave beams and packets with general astigmatism, Physical Review A 85(4) pap. 043835, 2012.

  • Kiselev A.P., Plachenov A.B., Chamorro-Posada P. Further generalizations of the Bateman solution. Novel wave beams and wave packets, Proc. Intern. Conf. Days on Diffraction 2012, IEEE, 124–128, 2012.

  • Babich V.M., Kiselev A.P. Elastic waves. A high-frequency theory. BHV, St. Peters­burg, 2014 (in Russian).

  • Tagirdzhanov A.M., Blagovestchenskii A.S., Kiselev A.P., Harmonic in time wavefields of ‘complex sources’ and their sources in the real space, J. Math. Sci. 206(3) 315–327, 2015.

  • Kiselev A.P., Tagirdzhanov A.M. Paradoxical properties of non-stationary wavefields of point sources in isotropic, elastic medium, Acoustical Phys. 61(4) 388–391, 2015.

  • Tagirdzhanov A.M., Kiselev A.P. Complexified spherical waves and their sources. A review, Optics & Spectroscopy 119(2) 271–281, 2015.

  • Tagirdzhanov A.M., Kiselev A.P. Gaussian wave packets based on “complex sources”, J. Math. Sci. 214(3) 372–381, 2016.

  • Kiselev A.P., Plachenov A.B. Laplace–Gauss and Helmholtz–Gauss paraxial modes in media with quadratic refraction index, J. Opt. Soc. Amer. A 33(4) 663–666, 2016.

  • Kiselev A.P., Plachenov A.B., Dyakova G.N. On the analyticity of waveforms in complexified relatively undistorted progressing waves, J. Electromagn. Waves & Appl. 31(13) 1325–1332, 2017.

  • Blagoveshchensky A.S., Kiselev A.P. A relation between two simple localized solutions of the wave equation, Comput. Math. Math. Phys. 57(6) 953–955, 2017.

  • Kiselev A.P. General elastic surface waves inanisotropic layered structures, J. Math. Sci. 224(1) 90–93, 2017.

  • Plachenov A.B., So I.A., Kiselev A.P. Paraxial Gaussian modes with simple astigmatic phases and nonpolynomial amplitudes, Proc. Intern. Conf. Days on Diffraction 2017, IEEE, 264–269, 2017.

  • Blagovestchenskii A.S., Kiselev A.P., Tagirdzhanov A.M. Simple solutions of the wave equation with a singularity at a running point, based on the complexified Bateman solution, J. Math. Sci. 224(1) 47–53, 2017.

  • Kiselev A.P. Time-harmonic Gaussian beams: Exact solutions of the Helmholtz equation in free space, Optics & Spectroscopy 123(6) 935–939, 2017; Erratum: 124(3) 450, 2018.

  • Babich V.M., Kiselev A.P. Elastic Waves: High-Frequency Theory, CRC Press, Taylor & Chapman, 305 p., 2018.

  • Blagoveshchensky A.S., Tagirdzhanov A.M., Kiselev A.P. On the Bateman–Hormander solution of the wave equation, having a singularity at a running point, Записки научных семинаров ПОМИ РАН 471, 76–85, 2018.

  • Kiselev A.P., Plachenov A.B. Astigmatic Gaussian beam: Exact solution of the Helmholtz equation, Proc. Intern. Conf. Days on Diffraction 2018, IEEE, 164–166 2018.

  • Zlobina E.A., Kiselev A.P. High-frequency diffraction by a contour with a jump of curvature, Proc. Intern. Conf. Days on Diffraction 2018, IEEE, 311–314, 2018.