Birth date: 19.04.1937
Keywords: mathematical methods of quantum mechanics; Schroedinger equation; spectral theory of linear operators; asymptotical methods of mathematical physics; wave propagation; nonlinear scattering.

Subject:

1) Mathematical scattering theory: trace formulas, asymptotic behavior of spectral characteristics, long-range potentials, singularities of many-particle scattering.

2) Asymptotical theory of classical wave propagation: scattering of short waves by convex obstacles, wave ropagation in wave guides.

3) Semiclassical approximation and the quantization: Maslov's operator, functional integrals, semiclassical approach to the adiabatically perturbed periodic problems, Bloch electrons in external fields, Stark–Wannie resonances semiclassical pseudodifferential operators with double discontinuous symbols and their applications to asymptotical study of the integrable models.

4) Difference equations with periodic coefficients: Semiclassical approach to Harper's equation, the monodromization instead of the monodromy.

5) Nonlinear waves: large time behavior of solutions of completely integrable equations, nonlinear scattering and the asymptotic stability of solitons for general nonlinear wave equations.

6) Main directions of current studies: Bloch electrons in externel fields, semiclassical approach to harper's equation, semiclassical pseudodifferential operators with discontinuous symbols, scattering of nonlinear waves.

Main publications:

• Formuly sledov i nekotorye asimptoticheskie otsenki yadra rezolventy dlya operatora Shredingera v trekhmernom prostranstve // Problemy matematicheskoi fiziki, LGU, 1966, vyp. 1, 82–101.
• Ob asimptoticheskom povedenii spektralnykh kharakteristik vneshnikh zadach dlya operatora Shredingera // Izv. AN SSSR, ser. matem., 1975, t. 39, # 1, 149–236.
• Kvaziklassicheskoe priblizhenie dlya uravnenii s periodicheskimi koeffitsientami // UMN, 1987, t. 62, vyp. 6, 77–98.
• Rasseyanie dlya nelineinogo uravneniya Shredingera: sostoyaniya, blizkie k solitonu // Algebra i analiz, t. 4, vyp. 6, 1992, 63–102 (sovm. s G. S. Perelman).
• Uravnenie Kharpera: monodromizatsiya bez kvaziklassiki // Algebra i analiz, 1996, t. 8, vyp. 2, 65–97 (sovm. s A. A. Fedotovym).

Publications in Math-Net.Ru

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Organisations:

• St. Petersburg State University, Mathematics and Mechanics Faculty
• St. Petersburg Mathematical Society
• St. Petersburg State University, Faculty of Physics
• V. A. Fock Institute of Physics, Saint-Petersburg State University