• 260 Citations
  • 9 h-Index
1974 …2019
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Research Output 1974 2019

  • 260 Citations
  • 9 h-Index
  • 97 Article
  • 11 Conference contribution
  • 2 Chapter
2019
1 Citation (Scopus)
decomposition
linear operators
operators
Cauchy problem
propagation
decomposition
operators
perturbation
Cauchy problem
infinity
Open Access
Reaction-diffusion Model
Population Model
Approximate Solution
Symmetry
Population dynamics
scalars
vacuum
kinetic energy
tensors
polarization
2018
3 Citations (Scopus)
linear equations
nonlinear equations
partial differential equations
formalism
intervals
asymptotic series
elliptic functions
differential equations
diffusion coefficient
perturbation
1 Citation (Scopus)
allowances
interactions

One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift

Shapovalov, A. V., 18 Apr 2018, (Accepted/In press) In : Russian Physics Journal. 60, 12, p. 1-10 10 p.

Research output: Contribution to journalArticle

Cauchy problem
symmetry
traveling waves
partial differential equations
iteration
1 Citation (Scopus)
Dirac equation
electromagnetic fields
electromagnetism
operators
symmetry
2017

Noncommutative Integrability of the Klein–Gordon and Dirac Equations in (2+1)-Dimensional Spacetime

Breev, A. I. & Shapovalov, A. V., 11 Mar 2017, (Accepted/In press) In : Russian Physics Journal. 59, 11, p. 1-6 6 p.

Research output: Contribution to journalArticle

Minkowski space
Dirac equation
wave equations
algebra

Quasistationary Solution of a Two-Component Hyperbolic System on an Interval

Isakov, K. A. & Shapovalov, A. V., 11 Jan 2017, (Accepted/In press) In : Russian Physics Journal. 59, 9, p. 1-8 8 p.

Research output: Contribution to journalArticle

hyperbolic systems
intervals
leakage
1 Citation (Scopus)
nonlinearity
symmetry
dynamical systems
differential equations
moments
2016
2 Citations (Scopus)
Parametric Solutions
Semiclassical Approximation
Curve
quasi-steady states
Circumference
1 Citation (Scopus)
nonlinearity
operators
symmetry
Cauchy problem
formalism
2 Citations (Scopus)

The Dirac equation in an external electromagnetic field: Symmetry algebra and exact integration

Breev, A. I. & Shapovalov, A. V., 25 Jan 2016, In : Journal of Physics: Conference Series. 670, 1, 012015.

Research output: Contribution to journalArticle

Dirac equation
electromagnetic fields
algebra
symmetry
operators

Thermal Action of the Nanoparticle Heated by Pulse-Periodic Laser Radiation on a Biotissue

Krainov, A. Y., Shapovalov, A. V. & Moiseeva, K. M., 1 Dec 2016, In : Russian Physics Journal. 59, 8, p. 1219-1224 6 p.

Research output: Contribution to journalArticle

laser beams
nanoparticles
pulses
heating
gold
2015
2 Citations (Scopus)

Analysis of the component composition of exhaled air using laser spectroscopy and canonical correlation analysis

Kistenev, Y. V., Borisov, A. V., Shapovalov, A. V. & Nikiforova, O. Y., 2015, 21st International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics. SPIE, Vol. 9680. 96804C

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Laser Spectroscopy
Canonical Correlation Analysis
Laser spectroscopy
laser spectroscopy
Absorption spectra
3 Citations (Scopus)

Applications of principal component analysis to breath air absorption spectra profiles classification

Kistenev, Y. V., Shapovalov, A. V., Borisov, A. V., Vrazhnov, D. A., Nikolaev, V. V. & Nikiforova, O. Y., 2015, International Conference on Atomic and Molecular Pulsed Lasers XII. SPIE, Vol. 9810. 98101Y

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pulmonary diseases
Data Preprocessing
Absorption Spectra
preprocessing
principal components analysis
perturbation
shift
1 Citation (Scopus)

Comparison of classification methods used for analysis of complex biological gas mixtures by means of laser spectroscopy

Kistenev, Y. V., Shapovalov, A. V., Vrazhnov, D. A., Nikolaev, V. V. & Nikiforova, O. Y., 2015, 21st International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics. SPIE, Vol. 9680. 968049

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Laser Spectroscopy
Laser spectroscopy
Gas Mixture
preprocessing
principal components analysis

Comparison of mathematical methods of geochemical data processing

Marfin, A., Lychagin, D. V., Shapovalov, A. V. & Alfyorova, E. A., 14 Sep 2015, IOP Conference Series: Materials Science and Engineering. 1 ed. Institute of Physics Publishing, Vol. 91. 012083

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fractal dimension
Chemical elements
Fractals
Statistical methods
4 Citations (Scopus)

Determination of component concentrations in models of exhaled air samples using principal component analysis and canonical correlation analysis

Kistenev, Y. V., Borisov, A. V. & Shapovalov, A. V., 2015, International Conference on Atomic and Molecular Pulsed Lasers XII. SPIE, Vol. 9810. 98101Z

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Canonical Correlation Analysis
Absorption Spectra
principal components analysis
Principal component analysis
Principal Component Analysis
elementary particles
physics
center of mass
operators
perturbation

Local conformational perturbations of the DNA molecule in the SG-model

Krasnobaeva, L. A. & Shapovalov, A. V., 17 Nov 2015, New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies". American Institute of Physics Inc., Vol. 1688. 030020

Research output: Chapter in Book/Report/Conference proceedingConference contribution

deoxyribonucleic acid
momentum
perturbation
molecules
Fokker-Planck equation

Quantitative comparison of the absorption spectra of the gas mixtures in analogy to the criterion of Pearson

Kistenev, Y. V., Kuzmin, D. A., Sandykova, E. A. & Shapovalov, A. V., 2015, 21st International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics. SPIE, Vol. 9680. 96803S

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gas Mixture
Absorption Spectra
Gas mixtures
gas mixtures
Analogy
approximation
wave packets
interactions

Solutions of nonlocal nonlinear diffusion equations in data filtering problems

Vrazhnov, D. A., Shapovalov, A. V. & Nikolaev, V. V., 17 Nov 2015, New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies". American Institute of Physics Inc., Vol. 1688. 030016

Research output: Chapter in Book/Report/Conference proceedingConference contribution

filters

Solutions of the Gross-Pitaevskii Equation in Prolate Spheroidal Coordinates

Borisov, A. V. & Shapovalov, A. V., Jan 2015, In : Russian Physics Journal. 57, 9, p. 1201-1209

Research output: Contribution to journalArticle

Statistical approach to the analysis of the composition of multicomponent gas mixtures using absorption laser spectroscopy

Kistenev, Y. V., Borisov, A. V. & Shapovalov, A. V., 2015, 21st International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics. SPIE, Vol. 9680. 968044

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Laser Spectroscopy
Absorption Spectroscopy
Laser spectroscopy
Gas Mixture
principal components analysis
1 Citation (Scopus)

Thermal interaction of biological tissue with nanoparticles heated by laser radiation

Krainov, A. Y., Moiseeva, K. M. & Shapovalov, A. V., 2015, International Conference on Atomic and Molecular Pulsed Lasers XII. SPIE, Vol. 9810. 981020

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Biological Tissue
Laser Radiation
Laser radiation
Nanoparticles
laser beams
1 Citation (Scopus)

Wavelet based de-noising of breath air absorption spectra profiles for improved classification by principal component analysis

Kistenev, Y. V., Shapovalov, A. V., Borisov, A. V., Vrazhnov, D. A., Nikolaev, V. V. & Nikiforova, O. Y., 17 Nov 2015, New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies". American Institute of Physics Inc., Vol. 1688. 030010

Research output: Chapter in Book/Report/Conference proceedingConference contribution

principal components analysis
absorption spectra
air
profiles
2014
7 Citations (Scopus)
Integrodifferential equations
Pattern Formation
Trajectories
Large Time Asymptotics
Integro-differential Equation
1 Citation (Scopus)
operators
symmetry
quadratic equations
linear equations
2 Citations (Scopus)
Dirac equation
algebra
symmetry
Yang-Mills fields
differential operators
2013

Assessment of tomsk region economic area

Kozlovskaya, O. V., Shapovalov, A. V. & Akerman, E. N., 2013, Mathematical Models of Non-linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere. Nova Science Publishers Inc, p. 461-468 8 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Economics
Factor Models
Recommendations
3 Citations (Scopus)
estimates
norms
intervals

SG-kink dynamics under dissipation and external regular and random forces

Krasnobaeva, L. A. & Shapovalov, A. V., 2013, Mathematical Models of Non-linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere. Nova Science Publishers Inc, p. 177-190 14 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Kink
Dissipation
Momentum
Nonlinear Fokker-Planck Equations
Fokker-Planck Equation
8 Citations (Scopus)
Gross-Pitaevskii Equation
Intertwining Operators
Nonlocal Equations
Symmetry
Operator
2012
7 Citations (Scopus)
Semiclassical Approximation
Integrodifferential equations
Integro-differential Equation
Nonlinearity
Symmetry
2011
3 Citations (Scopus)

Equivalent Lagrangian densities and invariant collective coordinates equations

Zamora-Sillero, E. & Shapovalov, A. V., 11 Feb 2011, In : Journal of Physics A: Mathematical and Theoretical. 44, 6, 065204.

Research output: Contribution to journalArticle

Partial differential equations
Invariant
Invariance
partial differential equations
Partial differential equation
5 Citations (Scopus)
two dimensional models
radii
interactions
rings
6 Citations (Scopus)

Numerical simulation of the one-dimensional population dynamics with nonlocal competitive losses and convection

Aleutdinova, V. A., Borisov, A. V., Shaparev, V. É. & Shapovalov, A. V., Sep 2011, In : Russian Physics Journal. 54, 4, p. 479-484 6 p.

Research output: Contribution to journalArticle

convection
normal density functions
simulation
polar coordinates
nonlinearity
approximation
Cauchy problem
Einstein equations
2009
1 Citation (Scopus)

Formalism of semiclassical asymptotics for a two-component Hartree-type equation

Smirnova, E. I., Trifonov, A. Y. & Shapovalov, A. V., 1 Oct 2009, In : Russian Physics Journal. 52, 10, p. 1068-1076 9 p.

Research output: Contribution to journalArticle

formalism
nonlinearity
trajectories
operators
matrices

Modulation of the velocity of soliton-like perturbations for the sine-Gordon equation with external force and dissipation

Krasnobaeva, L. A. & Shapovalov, A. V., 2009, In : Russian Physics Journal. 52, 12, p. 1331-1338 8 p.

Research output: Contribution to journalArticle

dissipation
solitary waves
modulation
perturbation
step functions
20 Citations (Scopus)
nonlinearity
approximation
operators
Cauchy problem
Einstein equations
2008

Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model

Krasnobaeva, L. A. & Shapovalov, A. V., Feb 2008, In : Russian Physics Journal. 51, 2, p. 158-167 10 p.

Research output: Contribution to journalArticle

dissipation
momentum
Fokker-Planck equation
distribution functions
nonlinear equations
5 Citations (Scopus)

Kink velocity in nonstationary external fields for the sine-Gordon model with allowance for dissipation effects

Krasnobaeva, L. A. & Shapovalov, A. V., Jan 2008, In : Russian Physics Journal. 51, 1, p. 89-98 10 p.

Research output: Contribution to journalArticle

allowances
dissipation
trends
step functions
numerical analysis
1 Citation (Scopus)
Nonlinear Fokker-Planck Equations
Fokker-Planck Equation
Cauchy Problem
Semiclassical Approximation
Asymptotic Solution
2007

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

Litvinets, F. N., Shapovalov, A. V. & Trifonov, A. Y., 7 Sep 2007, In : Journal of Physics A: Mathematical and Theoretical. 40, 36, p. 11129-11149 21 p., 013.

Research output: Contribution to journalArticle

Berry Phase
Linear equations
Magnetic Field
Magnetic fields
linear equations