Member in Editorial boards
- Mathematical Notes, Deputy Editor (Russian Academy of Sciences)
- Theoretical and Mathematical Physics (Russian Academy of Sciences)
- Russian Journal of Mathematical Physics (Nauka–Interperiodica, Russian Academy of Sciences)
Member in Academic (Graduation) Councils
- Steklov Mathematical Institute of Russian Academy of Sciences
- Moscow Institute of Electronics and Mathematics
- Faculty of Nanotechnologies and Informatics of
Moscow Institute of Physics and Technology
- Asymptotic methods and adiabatic approximations
in linear and nonlinear partial differential equations [1–9].
- Semiclassical methods in linear multidimensional spectral problems.
Equations of quantum mechanics. Tunnel effects. Quantum mechanics of
- Averaging, normal forms, and resonances [18–20].
- Wave propagation and propagation of singularities in linear
and nonlinear inhomogeneous media. Waves and vortices in
geophysical hydrodynamics [21–23].
- Linear and nonlinear water waves over nonuniform and
elastic bottom [24–30].
- Wave interactions and turbulence effects.
Navier-Stokes equations [31–33].
Some publications pertaining to the aforementioned topics A–F are listed below.
For the full list, which includes over 125 scientific papers,
see my CV.
- Finite-zone almost periodic solution in WKB-approximation (with V.P. Maslov), Sovremennye problemy matematiki, Itogi nauki i tekhniki, VINITI, No. 15, 1980. (J. Sov. Math., 16, No. 6, 1981, pp. 1433–1486.)
- Multi-phase asymptotics of nonlinear partial differential equations with a small parameter (with V.P. Maslov), Sov. Sci. Rev.–Math. Phys. Rev., Vol. 3, 1982, Overseas Publ. Association, pp. 221–311.
- Multidimensional Dirichlet series in a problem of asymptotic spectral series of nonlinear elliptic equations (with V.P. Maslov), Sovremennye problemy matematiki, Itogi nauki i tekniki. VINITI, No. 23, 1983. (J. Sov. Math., 28, No.1, 1985, pp. 91–143.)
- Resonances in asymptotic solutions of Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential, Math. Notes, Vol. 44, No. 3, 1988.
- Resonance correction for adiabatically perturbed finite-zone almost-periodic solution of KdV equation, Math. Notes, Vol. 44, No. 4, 1988, pp. 551–554.
- Basic systems on the torus generated by finite-zone integration of the KdV equation (with Yu.M. Vorob'ev), Math. Notes, Vol. 47, No. 1, 1990, pp. 32–41.
- Multi-phase solutions of Benjamin–Ono equation and their averaging (with I.M. Krichever), Math. Notes, Vol. 49, No. 6, 1991, pp. 583–595.
- Resonances in multi-frequency averaging theory of nonlinear partial differential equations, in Singular Limits of Dispersive Waves, N.M.Ercolani et al., Eds., NATO ASI Series, Ser.B, Vol. 320, Plenum Press, NY, 1994, pp. 203–217.
- Operator separation of variables for adiabatic problems in quantum and wave mechanics (with V.V. Belov and T.Ya. Tudorovskiy), J. Engng. Math, Vol. 55, No. 1–4, 2006, pp. 183–237.
- Some application of the complex germ theory to equations with a small parameter (with V.P. Maslov), Sovremennye Problemi Matematiki, Itogi Nauki i Tehniki, VINITI, Vol. 5, 1975, pp. 141–211. (J. Sov. Math., Vol. 5, 1976, pp. 552–605.)
- Semiclassical Maslov asymptotics with complex phases. I (with V.V. Belov), Theor. Math. Phys., Vol. 92, No. 2, 1992, pp. 843–868.
- Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation (with V.N. Kolokol'tsov and V.P.Maslov), Theor. Math. Phys., Vol. 87, No. 3, 1991, pp. 561–602.
- The double-well splitting of the low energy discrete Φ4-models on tori (with V.N. Kolokol'tsov), J. Math. Phys., Vol. 36, No. 3, 1995, pp. 1038–1053.
- On Quasimodes of Small Diffusion Operators Corresponding to Stable Invariant Tori with Nonregular Neighborhoods (with S. Albeverio and M. Poteryakhin), Asymptotic Analysis, Vol. 43, No. 3, 2005, pp. 171–203.
- The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. I, II (with J. Brüning and K.V. Pankrashkin), Russ. J. Math. Phys., Vol. 9, 2002, No. 1, pp. 14–49; No. 3, pp. 400–416.
- Hall conductivity of minibands lying at the wings of Landau levels (with J. Brüning, V.A. Geyler, and K.V. Pankrashkin), JETP Letters, Vol. 77, No. 11 , 2003, pp. 616–618.
- Generalized adiabatic principle for electron dynamics in curved nanostructures (with V.V. Belov, V.P. Maslov, and T.Ya. Tudorovskii), Uspekhi Fizicheskikh Nauk, Vol. 175, No. 9, 2005, 1004–1010. (Physics-Uspekhi, Vol. 48, No. 9, 2005, pp. 962–968.)
- Explicit formulas for action–angle variables in the neighborhood of an isotropic torus and their applications (with V.V. Belov and V.A. Maksimov), Teor. Mat. Fizika, Vol. 135, No. 3, 2003, pp. 378–408. (Theor. Math. Phys. Vol. 135, No. 3, 2003, pp. 765–791.)
- On averaging for Hamiltonian system with one fast phase and small amplitudes (with J. Brüning and M. Poteryakhin), Mat. Zametki, Vol. 70, No. 5, 2001, pp. 660–669. (Math. Notes, Vol. 70, No. 5, 2001, pp. 599–607.)
- Isotropic tori, complex germ and Maslov index, normal forms and quasimodes of multidimensional spectral problems (with V.V. Belov and O.S. Dobrokhotov), Math. Notes, Vol. 69, 2001, No. 4, pp. 437–466.
- Asymptotic rapidly decreasing solution of linear, strictly hyperbolic systems with variable coefficients (with V.P. Maslov, P.N. Zhevandrov, and A.I. Shafarevich), Math. Notes, 1991, Vol. 49, No. 4, pp. 355–365.
- An example of calculation of the trajectory of typhoon, based on V.P.Maslov conjecture (with V.V. Bulatov, V.V. Vladimirov, and V.G. Danilov), Dokl. Akad. Nauk (Geophysics), 1994, v .338, No. 1, pp. 102–105 (Phys. Doklady)
- Hugoni\'ot–Maslov Chains for Solitary Vortices of the Shallow Water Equations. I, II, Russ. J. Math. Phys., Vol. 6, 1999, No. 2, pp. 137–173; 1999, No. 3, pp. 282–313.
- Maslov's methods in linearized theory of gravitational waves on the liquid surface, Dokl. Akad. Nauk SSSR, Vol. 269, No. 1, 1983, pp. 76–80. (Sov. Phys. Doklady Vol. 28, 1983,pp. 229–231.)
- Nonstandard characteristics and Maslov's operational method in linear problems of unsteady water waves (with P.N. Zhevandrov), Funct. Anal. Appl., Vol. 19,No. 4, 1985,pp. 285–295.
- Asymptotic behavior of water surface waves trapped by shores and irregularities of the bottom relief, Sov. Phys. Doklady Vol. 31, No. 7, 1986, pp. 537–539.
- Operator model of the problem of liquid vibrations on the elastic bottom (with R.O. Griniv and A.A. Shkalikov), Math. Notes, Vol. 68, No. 1, 2000.
- Asymptotic expansions and the Maslov canonical operator in the linear theory of water waves. I (with P.N. Zhevandrov), Russ. J. Math. Phys., Vol. 10, No. 1, 2003, pp. 1–31.
- Description of tsunami propagation based on the Maslov canonical operator (with S. Sekerzh-Zenkovich, B. Tirozzi, and T. Tudorovskii), Dokl. Akad. Nauk, 2006, Vol. 409, No. 2, pp. 171–175. (Doklady Mathematics, 2006, Vol. 74, No. 1, pp. 592–596.)
- Localized Wave and Vortical Solutions to Linear Hyperbolic Systems and Their Application to the Linear Shallow Water Equations (with A.I. Shafarevich and B. Tirozzi), Russ. J. Math. Phys., Vol. 15, No. 2, (2008), pp. 192–221.
- Parametrix and asymptotic local solutions of Navier–Stokes Equations in R3 linearized on a smooth flow (with A.I. Shafarevich), Math. Notes, 1992, Vol. 51, No. 1,1992,pp. 47–54.
- Asymptotic solutions of linearized Navier–Stokes equation (with A.I. Shafarevich), Math. Notes, Vol. 53, No. 1,1993, pp. 19–26.
- Magnetic field asymptotics in a well conducting fluid (with V. Martinez Olive, A. Ruzmaikin, and A. Shafarevich), Geophysical and Astrophysical Fluid Dynamics, vol. 82, 1996, pp. 255–280.