head of the Institute of High Technology
professor
Cosmology and relativity
Quantum and classical field theory
HighEnergy Physics
Nonlinear partial differental equations
Integrable systems of the quantum mechanics and the field theory
Inverse scattering transformation method and connected methods: Backlund Transformation, Darboux transformation, finitegap 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 nationwide 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
Sofia Kovalevskay Northwestern Center of Mathematical Studies 

Since 2021 
Head of Scientific and Educational Mathematical Center 
Immanuel Kant Baltic Federal University  
Since 2021  Head of Education and Research Cluster “Institute of High Technology” 
2016–2021 
Director of the Institute of Mathematics, Physics and IT 
2013–2016  ViceRector 
Since 1993  Assistant Professor of the Baltic Institute of Economics and Finances 
Immanuel Kant Baltic Federal University, Theoretical Physics Department  
2003–2013 
Chairman 
1993–2003 
Assistant Professor 
1991–1993 
Teaching Assistant 
Immanuel Kant Baltic Federal University & St.Petersburg State University 

1989–1991  Graduate Student, Teaching Assistant and Research Fellow 
Field theory:
It is proved that the selfaction potential for a scalar field can be reconstructed from the scattering data for a oneloop potential describing quantum fluctuations [44]. 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 [39]. Generalized nonsingular Fabini instantons for the nonlinear KleinGordon equation with a negative coupling constant are constructed and it is proved that they exist only in the Euclidean space with dimension D<6 [31].
Twodimensional hydrodynamics:
An analogue of the Darboux transformations for the twodimensional Euler equation [43] and in MONOGRAPHS [3] is constructed and an algebraic approach is developed for constructing exact solutions of the twodimensional NavierStokes equation [36].
Cosmology:
In 2003, the author discovered the phenomenon of smooth phantomization [26, astroph/ 0305019]. Using the Darboux transformations, a method was developed for constructing all known and a number of new exact nonsingular solutions describing a threedimensional brane interacting with fivedimensional gravity [38]. 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 [33]. An unexpected and useful connection between the Friedmann equations and the Abel equation of the first type [28], [17] is found. A new type of cosmological singularities with a finite value of the scale factor [27] is found and a separate class of cosmological singularities of the first kind [8] 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 [6].
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