• 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
Filter
Article
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
perturbation
shift
elementary particles
physics
center of mass
operators
perturbation
approximation
wave packets
interactions

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

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
3 Citations (Scopus)
estimates
norms
intervals
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
16 Citations (Scopus)

Formation, control, and dynamics of N localized structures in the Peyrard-Bishop model

Zamora-Sillero, E., Shapovalov, A. V. & Esteban, F. J., 6 Dec 2007, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 76, 6, 066603.

Research output: Contribution to journalArticle

Localized Structures
Formation Control
nonlinear equations
Nonlinear Equations
Initial conditions

Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation

Lisok, A. L., Trifonov, A. Y. & Shapovalov, A. V., 1 Jul 2007, In : Russian Physics Journal. 50, 7, p. 695-709 15 p.

Research output: Contribution to journalArticle

trajectories
operators
energy
approximation
2 Citations (Scopus)

Soliton fractals in the Korteweg-de Vries equation

Zamora-Sillero, E. & Shapovalov, A. V., 29 Oct 2007, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 76, 4, 046612.

Research output: Contribution to journalArticle

Solitary Waves
Korteweg-de Vries Equation
Solitons
Fractal
fractals
6 Citations (Scopus)
Kolmogorov Equation
Nonlinearity
Symmetry
Operator
Linear equation
2006
polar coordinates
strokes
nonlinear equations
approximation
solitary waves
8 Citations (Scopus)

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

Litvinets, F. N., Shapovalov, A. V. & Trifonov, A. Y., 3 Feb 2006, In : Journal of Physics A: Mathematical and General. 39, 5, p. 1191-1206 16 p.

Research output: Contribution to journalArticle

Berry Phase
Gross-Pitaevskii Equation
Nonlocal Equations
linear equations
Countable
2005
9 Citations (Scopus)
Gross-Pitaevskii Equation
Nonlocal Equations
Exact Solution
Symmetry
Operator
15 Citations (Scopus)

One- and two-soliton solutions of the sine-Gordon equation as applied to DNA

Yakushevich, L. V., Krasnobaeva, L. A., Shapovalov, A. V. & Quintero, N. R., 2005, In : Biophysics. 50, 3, p. 404-409 6 p.

Research output: Contribution to journalArticle

Polynucleotides
DNA
Vibration
1 Citation (Scopus)

Symmetry operators of a Hartree-type equation with quadratic potential

Lisok, A. L., Trifonov, A. Y. & Shapovalov, A. V., 1 Jan 2005, In : Siberian Mathematical Journal. 46, 1, p. 119-132 14 p.

Research output: Contribution to journalArticle

Symmetry
Operator
Nonlinear Integro-differential Equations
Periodic Potential
Evolution Operator

The nonlinear schrodinger equation for a many-dimensional system in an oscillator field

Borisov, A. V., Trifonov, A. Y. & Shapovalov, A. V., 1 Jul 2005, In : Russian Physics Journal. 48, 7, p. 746-753 8 p.

Research output: Contribution to journalArticle

strokes
nonlinear equations
oscillators
apexes
solitary waves
2 Citations (Scopus)
Gross-Pitaevskii Equation
Semiclassical Approximation
Evolution Operator
Stroke
Transverse
2004

Green's function of a hartree-type equation with a quadratic potential

Lisok, A. L., Trifonov, A. Y. & Shapovalov, A. V., 1 Nov 2004, In : Theoretical and Mathematical Physics. 141, 2, p. 1528-1541 14 p.

Research output: Contribution to journalArticle

Green's function
Green's functions
operators
Symmetry
Cauchy problem
Atoms
approximation
Electron energy levels
atoms
Vortex flow