head of the Institute of High Technology
Sofia Kovalevskay Northwestern Center of Mathematical Studies
Head of Scientific and Educational Mathematical Center
|Immanuel Kant Baltic Federal University|
|Since 2021||Head of Education and Research Cluster “Institute of High Technology”|
Director of the Institute of Mathematics, Physics and IT
|Since 1993||Assistant Professor of the Baltic Institute of Economics and Finances|
|Immanuel Kant Baltic Federal University, Theoretical Physics Department|
Immanuel Kant Baltic Federal University & St.-Petersburg State University
|1989–1991||Graduate Student, Teaching Assistant and Research Fellow|
Cosmology and relativity
Quantum and classical field theory
Non-linear partial differental equations
Integrable systems of the quantum mechanics and the field theory
Inverse scattering transformation method and connected methods: Backlund Transformation, Darboux transformation, finite-gap integration
Member of Presidium of Russian Gravitational Society
Included in “Who’s Who in the World», 2000
Medal awarded by the Russian Education Ministry for the best nation-wide PhD thesis (PhD thesis by S. D. Vereschagin) supervision in natural sciences and humanities, 2000
Honorary title: Honourable Worker of Higher Education and Vocational Training, 2012
It is proved that the self-action potential for a scalar field can be reconstructed from the scattering data for a one-loop potential describing quantum fluctuations . It is proved that the spatiotemporal noncommutativity leads to the generation of new bound states. It has been found that in the case of singular solutions, an infinite number of bound states arise with a spectrum similar to the spectrum of quark states . Generalized non-singular Fabini instantons for the nonlinear Klein-Gordon equation with a negative coupling constant are constructed and it is proved that they exist only in the Euclidean space with dimension D<6 .
An analogue of the Darboux transformations for the two-dimensional Euler equation  and in MONOGRAPHS  is constructed and an algebraic approach is developed for constructing exact solutions of the two-dimensional Navier-Stokes equation .
In 2003, the author discovered the phenomenon of smooth phantomization [26, astro-ph/ 0305019]. Using the Darboux transformations, a method was developed for constructing all known and a number of new exact non-singular solutions describing a three-dimensional brane interacting with five-dimensional gravity . It is shown that it is impossible to accurately predict the future dynamics of the universe using only astronomical data on the evolution of the scale factor, no matter how accurate these data are . An unexpected and useful connection between the Friedmann equations and the Abel equation of the first type ,  is found. A new type of cosmological singularities with a finite value of the scale factor  is found and a separate class of cosmological singularities of the first kind  is studied. A new cosmological model has been proposed in which quantum effects manifest themselves on cosmological scales and lead to a hypothetical phantom component of dark energy .
Личный кабинет для