Persons: Shapovalov Alexander Vasilevich, List of publications

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Shapovalov Alexander Vasilevich

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2025
1.	A. E. Kulagin, A. V. Shapovalov, “Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation”, The European Physical Journal Plus, 140 (2025), 246 , 23 pp. https://link.springer.com/article/10.1140/epjp/s13360-025-06183-6, arXiv: 2408.08532 [math-ph]
2.	A. V. Shapovalov, S. A. Siniukov, “Quasiparticle solutions to the 1D nonlocal Fisher–KPP equation with a fractal time derivative in the weak diffusion approximation”, Fractal Fract., 9:5 (2025), 279 , 24 pp. https://www.mdpi.com/2504-3110/9/5/279, arXiv: math-ph/ 2503.15099 $https://doi.org/10.3390/fractalfract9050279$
3.	M. A. Vologzhin, L. A. Krasnobaeva, A. V. Shapovalov, “Issledovanie dinamiki konformatsionnogo vozmuscheniya v molekule DNK v modeli Muto”, Izvestiya vuzov. Fizika, 68:4 (2025), 5–13
4.	A. V. Shapovalov, A. E. Kulagin,, “Kvaziklassicheskii podkhod dlya obobschennogo uravneniya Khausa, opisyvayuschego izluchenie v rezonatore lazera s impulsnoi nakachkoi”, Izvestiya vuzov. Fizika, 68:3 (2025), 90–97 https://journals.tsu.ru/physics/&journal_page=archive&id=2588

2024
5.	A. I. Breev, K. V. Vasilev, A. V. Shapovalov, “Rasshirenie simmetrii i obobschennye invariantno-gruppovye resheniya uravneniya teploprovodnosti i uravneniya Byurgersa”, Izvestiya vuzov. Fizika, 67:1 (2024), 99–108
6.	A. E. Kulagin, A. V. Shapovalov, “Kvaziklassicheskie kvazichastitsy dlya uravneniya Shredingera s nelokalnoi nelineinostyu i antiermitovoi chastyu”, Voronezhskaya zimnyaya matematicheskaya shkola S.G. Kreina – 2024 : materialy mezhdunarodnoi Voronezhskoi zimnei matematicheskoi shkoly, posvyaschennoi pamyati V. P. Maslova. (Voronezh, 26–30 yanvarya 2024 g.), 317 c. ISBN 978–5–9273–3692–0, Izdatelskii dom VGU, Voronezh, 2024, s. 130–132 https://vzms.kmm-vsu.ru/files/vzms_2024.pdf
7.	A. E. Kulagin, A. V. Shapovalov, “A semiclassical approach to the nonlocal nonlinear Schrodinger equation with a non-Hermitian term”, Mathermatics, 12:4 (2024), 580 , 22 pp. https://www.mdpi.com/2227-7390/12/4/580, arXiv: 2308.08286
8.	A. V. Shapovalov, A. E. Kulagin, S. A. Sinyukov, “Nevyazka kvaziklassicheski sosredotochennykh reshenii kineticheskogo uravneniya na primere nelokalnoi modeli ionizatsii aktivnoi sredy”, Izvestiya vuzov. Fizika, 67:2 (2024), 36–44
9.	A. E. Kulagin, A. V. Shapovalov, “Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation”, Physica Scripta, 99:4 (2024), 045228 , 15 pp. https://iopscience.iop.org/article/10.1088/1402-4896/ad302c, arXiv: 2309.02129
10.	V. V. Obukhov, K. E. Osetrin, A. V. Shapovalov, “Comments on the article 'M.O. Katanaev, Complete separation of variables in the geodesic Hamilton-Jacobi equation in four dimensions, Physica Scripta (2023), 98, 104001'”, Physica Scripta, 99:6 (2024), 067002 , 4 pp.
11.	S. A. Sinyukov, A. E. Kulagin, A. V. Shapovalov, “Dinamicheskaya sistema momentov dlya nelokalnogo uravneniya Fishera – Kolmogorova – Petrovskogo – Piskunova s drobnoi proizvodnoi po vremeni v priblizhenii slaboi diffuzii”, Izvestiya vuzov. Fizika, 67:8 (2024), 5–14
12.	A. V. Shapovalov, S. A. Siniukov, “Fractal dynamics of solution moments for the KPP–Fisher equation”, Russian Physics Journal, 67 (2024), 1827–1837

2023
13.	A. V. Shapovalov, A. I. Breev, “Harmonic Oscillator Coherent States from the Standpoint of Orbit Theory”, Symmetry, 15:2 (2023), 282 , 11 pp., arXiv: quant-ph/2211.11029
14.	A. E. Kulagin, A. V. Shapovalov, “Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain”, Mathermatics, 11:3 (2023), 584 , 18 pp. https://www.mdpi.com/2227-7390/11/3/584, arXiv: 2208.03014v2 [math.PR]
15.	A. V. Shapovalov, “On equivalence between kinetic equations and geodesic equations in spaces with affine connection”, Symmetry, 15:4 (2023), 905 , 16 pp. https://www.mdpi.com/2073-8994/15/4/905
16.	V. N. Zadorozhnyi, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie. Chast III. 4. Integralnoe ischislenie funktsii neskolkikh peremennykh, v. III, Integralnoe ischislenie funktsii neskolkikh peremennykh., eds. prof. V. Ya. Epp, prof. V. N. Cherepanov, Izd-vo TPU, Tomsk, 2023 , 502 pp.

2022
17.	I. Brevik, A. V. Shapovalov, “Effects of low concentration in aqueous solutions within the fractal approach”, Russian Physics Journal, 65:2 (2022), 197–207 https://link.springer.com/article/10.1007/s11182-022-02623-3
18.	A. V. Shapovalov, A. E. Kulagin, S. A. Siniukov, “Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity”, Symmetry, 14:3 (2022), 577 , 20 pp., arXiv: math-ph/2203.02333
19.	T. V. Gandzha, K. A. Isakov, A. V. Shapovalov, “Analysis of the kinetic model of a single-stage process for obtaining titanium dioxide”, Russian Physics Journal, 65:4 (2022), 663–670 https://link.springer.com/article/10.1007/s11182-022-02682-6
20.	A. V. Shapovalov, A. E. Kulagin, S. A. Siniukov, “Pattern formation in a nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov model and in a nonlocal model of the kinetics of an metal vapor active medium”, Russian Physics Journal, 65:4 (2022), 695–702 https://link.springer.com/article/10.1007/s11182-022-02687-1
21.	A. I. Breev, A. V. Shapovalov, D. M. Gitman, “Noncommutative reduction of nonlinear Schrödinger equation on Lie groups”, Universe, 8:9 (2022), 445 , 13 pp. https://www.mdpi.com/2218-1997/8/9/445, arXiv: 2108.05180v2 [math-ph]

2021
22.	A. V. Shapovalov, R. Brons, “Invariance properties of the one-dimensional diffusion equiation with a fractal time derivative”, Russian Physics Journal, 64:4 (2021), 704–716
23.	A. E. Kulagin, A. V. Shapovalov, A. Yu. Trifonov, “Semiclassical spectral series localized on a curve for the GrossPitaveskii equation with a nonlocal interaction”, Symmetry, 13:7 (2021), 1289 , 22 pp.
24.	A. I. Breev, A. V. Shapovalov, Noncommutative reduction of the nonlinear Schrodinger equation on Lie groups, 2021 , 19 pp., https://arxiv.org/abs/2108.05180, arXiv: math-ph/2108.05180v1
25.	S. A. Siniukov, A. Yu. Trifonov, A. V. Shapovalov, “Examples of asymptotic solutions obtained by the complex germ method for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Russian Physics Journal, 64:8 (2021), 1542–1552
26.	A. V. Shapovalov, A. E. Kulagin, “Semiclassical approach to the nonlocal kinetic model of metal vapor aqctive media”, Mathematics, 9:23 (2021), 2995 , 16 pp., arXiv: math-ph/2111.05074v1

2020
27.	Alexander V. Shapovalov, Anton E. Kulagin, Andrey Yu. Trifonov, “The Gross–Pitaevskii equation with a nonlocal interaction in a semiclassical approximation on a curve”, Symmetry, 12:2 (2020), 201 , 25 pp. https://www.mdpi.com/2073-8994/12/2/201
28.	A. I. Breev, A. V. Shapovalov, “Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces”, Symmetry, 12:11 (2020), 1867 , 30 pp. https://www.mdpi.com/2073-8994/12/11/1867, arXiv: math-ph/2011.06401

2019
29.	A. V. Shapovalov, A. Yu. Trifonov, “Approximate solutions and symmetry of a two-component nonlocal reaction-diffusion population model of the Fisher–KPP type”, Symmetry, 11:3 (2019), 366 ;19 pp. https://www.mdpi.com/2073-8994/11/3/366/htm
30.	A. V. Shapovalov, A. Yu. Trifonov, “Adomian decomposition method for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Russian Physics Journal, 62:4 (2019), 710–719
31.	A. V. Shapovalov, A. Yu. Trifonov, “Adomyan decomposition method for a two component nonlocal reaction-diffusion model of the Fisher–Kolmogorov–Petrovskii–Piskunov type”, Russian Physics Journal, 62:5 (2019), 835–847
32.	A. I. Breev, A. V. Shapovalov, “Vacuum quantum effects on Lie groups with bi-invariant metrics”, International Journal of Geometric Methods in Modern Physics (IJGMMP), 16:8 (2019), 1950122 , 25 pp., arXiv: 1906.01826v1 [gr-qc]

2018
33.	A. V. Shapovalov, A. I. Breev, “Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field”, International Journal of Geometric Methods in Modern Physics, 15:5 (2018), 1850085 , 26 pp., arXiv: math-ph/1709.04644
34.	A. V. Shapovalov, A. Yu. Trifonov, “An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation”, International Journal of Geometric Methods in Modern Physics, 15:6 (2018), 1850102 , 30 pp., arXiv: math.AP/1409.3158
35.	A. V. Shapovalov, V. V. Obukhov, “Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher–KPP Model”, Symmetry, 10:3 (2018), 53 , 26 pp. http://www.mdpi.com/2073-8994/10/3/53/html
36.	Yu. V. Kistenev, A. V. Borisov, M. A. Titarenko, O. D. Baydik, A. V. Shapovalov, “Diagnosis of oral lichen planus from analysis of saliva samples using terahertz time-domain spectroscopy and chemometric”, Journal of Biomedical Optics, 23:4 (2018), 045001 , 8 pp.
37.	A. V. Shapovalov, V. V. Obukhov, “Influence of the environment on pattern formation in the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov model”, Russian Physics Journal, 61:6 (2018), 1093-1099 https://link.springer.com/article/10.1007/s11182-018-1501-8; https://rdcu.be/84br

2017
38.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity”, Russian Physics Journal, 60:2 (2017), 284–291 https://link.springer.com/article/10.1007
39.	Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, O. D. Baydik, M. A. Titarenko, “Diagnostics of oral lichen planus based on analysis of volatile organic compounds in saliva”, Dynamics and Fluctuations in Biomedical Photonics XIV (San Francisco, California, United States \| January 28, 2017), Proc. SPIE, 10063, 2017, 100630R , 7 pp. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2608918&resultClick=1
40.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie.Chast III. 3. Integralnoe ischislenie funktsii odnoi peremennoi, eds. d.f.-m.n., prof. Osetrin K.E., d.f.-m.n., prof. Bagrov V.G., Natsionalnyi issledovatelskii Tomskii politekhnicheskii universitet, Tomsk, 2017 , 494 pp.
41.	A. I. Breev and A. V. Shapovalov, Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field, 2017 , 24 pp., arXiv: arXiv:1709.04644v1

2018
42.	A. V. Shapovalov, “Approximate solutions of the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with quasilocal competitive losses”, Russian Physics Journal, 60:9 (2018), 1461–1468
43.	A. V. Shapovalov, “One-dimensional Fokker–Planck equation with quadratically nonlinear quasilocal drift.”, Russian Physics Journal, 60:12 (2018), 2063–2072 https://link.springer.com/article/10.1007/s11182-018-1327-4

2016
44.	A. I. Breev and A. V. Shapovalov, “The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration”, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23) (Prague, 23-27 June 2015), Journal of Physics: Conference Series, 670, 2016, 012015 , 12 pp. http://iopscience.iop.org/1742-6596/670/1/012015
45.	A. V. Shapovalov, A. Yu. Trifonov, and A. L. Lisok, “Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity”, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23) (Prague, 23-27 June 2015), Journal of Physics: Conference Series, 670, 2016, 012046 , 13 pp. http://iopscience.iop.org/article/10.1088/1742-6596/670/1/012046
46.	A. I. Breev, A. V. Shapovalov, A. V. Kozlov, “Integration the relativistic wave equations in bianchi ix cosmology model”, Computer Research and Modeling, 8:3 (2016), 433–443
47.	E. A. Levchenko , A. V. Shapovalov, A. Yu. Trifonov, “Asymptotics semiclassically concentrated on curves for the nonlocal Fisher– Kolmogorov–Petrovskii–Piskunov equation”, J. Phys. A: Math. Theor., 49 (2016), 305203 , 17 pp. http://iopscience.iop.org/article/10.1088/1751-8113/49/30/305203/meta
48.	A. Yu. Krainov, A. V. Shapovalov, A.V., and K. M. Moiseeva, “Thermal Action of the Nanoparticle Heated by Pulse-Periodic Laser Radiation on a Biotissue”, Russian Physics Journal, 59:8 (2016), 1219-1224

2017
49.	K. A. Isakov, A. V. Shapovalov, “Quasistationary solutions of a two-component hyperbolic system on an interval”, Russian Physics Journal, 59:9 (2017), 1349–1356
50.	A. .I. Breev and A. V. Shapovalov, “Noncommutative integrability of the Klein-Gordon and Dirac equations in (2+1)-dimensional spacetime”, Russian Physics Journal, 59:11 (2017), 1956–1961 http://link.springer.com/article/10.1007/s11182-017-1001-2

2016
51.	Yu. V. Kistenev, A. V. Shapovalov, D. A. Vrazhnov, V. V. Nikolaev, “Kalman filtering in the problem of noise reduction in the absorption spectra of exhaled air”, 22nd International Symposium Atmospheric and Ocean Optics: Atmospheric Physics (Tomsk, Russian Federation \| June 30, 2016), Proc. SPIE, 10035, 2016, 100350A , 6 pp.
52.	Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, A. I. Knyazkova, “Possibilities of laser spectroscopy for monitoring the profile dynamics of the volatile metabolite in exhaled air”, Proc. SPIE, 10035 (2016), 100350B , 6 pp.

2015
53.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie dlya mnogomernogo nelokalnogo uravneniya Fishera–Kolmogorova–Petrovskogo–Piskunova”, Kompyuternye issledovaniya i modelirovanie, 7:2 (2015), 205 – 219 http://crm.ics.org.ru/journal/issue/165/
54.	A. A. Prozorov, A. Yu. Trifonov, and A. V. Shapovalov, “Asymptotic behavior of the one-dimensional Fisher–Kolmogorov–Pertovskii–Piskunov equation with anomalous diffusion”, Russian Physics Journal, 58:3 (2015), 399–409 http://link.springer.com/article/10.1007/s11182-015-0514-9
55.	A. E. Kulagin, A. Yu. Trifonov, A. V. Shapovalov, “Quasiparticles described by the Gross-Pitaevskii equation in the semiclassical approximation”, Russian Physics Journal, 58:5 (2015), 606–615 (to appear)
56.	E. A. Levchenko, A. Yu. Trifonov., A. V. Shapovalov, “Asymptotics of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation near a quasistationary solution”, Russian Physics Journal, 58:7 (2015), 952-958
57.	A. I. Breev, A. V. Shapovalov, “Polyarizatsiya vakuuma skalyarnogo polya na gruppakh Li s biinvariantnoi metrikoi”, Kompyuternye issledovaniya i modelirovanie, 7:5 (2015), 989– 999
58.	A. V. Breev, A. V. Shapovalov, The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration, 2015 , 17 pp., http://arxiv.org/abs/1509.08612, arXiv: 1509.08612 [math-ph]
59.	A. Marfin, D. V. Lychagin, A. Shapovalov, E. A. Alfiorova, “Comparison of mathematical methods of geochemical data processing”, IOP Conf. Series: Materials Science and Engineering, 91 (2015), 012083 , 7 pp.
60.	L. A. Krasnobaeva, A. V. Shapovalov, “Local conformational perturbations of the DNA molecule in the SG-model”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030020 (Published online) , 6 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936015
61.	Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, D. A. Vrazhnov, V. V. Nikolaev, O. Yu. Nikiforova, “Wavelet based de-noising of breath air absorption spectra profiles for improved classification by principal component analysis”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030010 (Published online) , 5 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936005
62.	D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Solutions of nonlocal nonlinear diffusion equations in data filtering problems”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030016 (Published online) , 6 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936011
63.	A. Y. Krainov ; K. M. Moiseeva ; A. V. Shapovalov, “Thermal interaction of biological tissue with nanoparticles heated by laser radiation”, Proc. SPIE 9810, International Conference on Atomic and Molecular Pulsed Lasers XII, 981020 (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, 9810, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 981020-1-7 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478143&resultClick=1
64.	Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, D. A. Vrazhnov, V. V. Nikolaev, O. Y. Nikiforova, “Applications of principal component analysis to breath air absorption spectra profiles classification”, Proc. SPIE 9810, International Conference on Atomic and Molecular Pulsed Lasers XII, 98101Y (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 98101Y-1-6 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478141&resultClick=1
65.	Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, “Determination of component concentrations in models of exhaled air samples using principal component analysis and canonical correlation analysis”, Proc. SPIE 9810, XII International Conference on Atomic and Molecular Pulsed Lasers, 98101Z (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, 9810, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 98101Z-1-6 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478142&resultClick=1
66.	Yu. V. Kistenev, D. A. Kuzmin, E. A. Sandykova, A. V. Shapovalov, “Quantitative comparison of the absorption spectra of the gas mixtures in analogy to the criterion of Pearson”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 96803, eds. Oleg A. Romanovskii, SPIE, 2015, 96803S-1-8 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473089&resultClick=1
67.	Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, “Statistical approach to the analysis of the composition of multicomponent gas mixtures using absorption laser spectroscopy”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 968044 (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), 968044, eds. Oleg A. Romanovskii, SPIE, 2015, 968044-1-6 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473101&resultClick=1
68.	Yu. V. Kistenev, A. V. Shapovalov, D. A. Vrazhnov, V. V. Nikolaev, O. Y. Nikiforova, “Comparison of classification methods used for analysis of complex biological gas mixtures by means of laser spectroscopy”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 968049 (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 9680, eds. Oleg A. Romanovskii, SPIE, 2015, 96804C-1-6 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473106&resultClick=1
69.	Yury V. Kistenev, Alexey V. Borisov, Alexander V. Shapovalov, Olga Y. Nikiforova, “Analysis of the component composition of exhaled air using laser spectroscopy and canonical correlation analysis”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 96804C (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 9680, eds. Oleg A. Romanovskii, SPIE, 2015, 96804C-1-6 http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473109&resultClick=1
70.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical approximation for the nonlocal multidimensionalfisher-kolmogorov-petrovskii-piskunov equation”, Computer Research and Modeling, 7:2 (2015), 205–219
71.	A. I. Breev, A. V. Shapovalov, “Vacuum polarization of scalar field on lie groups with bi-invariantmetric”, Computer Research and Modeling, 7:5 (2015), 989–999

2014
72.	E. A. Levchenko, A. V. Shapovalov, and A. Yu. Trifonov, “Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Journal of Physics A: Mathematical and Theoretical, 47 (2014), 025209 , 20 pp. http://iopscience.iop.org/1751-8121/47/2/025209/article, arXiv: arXiv:1306.3765v1

2015
73.	A. V. Borisov, A. V. Shapovalov, “Solutions of the Gross–Pitaevskii equation in prolate spheroidal coordinates”, Russian Physics Journal, 57:9 (2015), 1201-1209 http://link.springer.com/article/10.1007/s11182-015-0364-5

2014
74.	A. I. Breev, A. V. Shapovalov, Yang-Mills gauge fields conserving symmetry algebra of Dirac equation in homogeneous space, 2014 , 25 pp., http://arxiv.org/abs/1406.5033, arXiv: gr-qc/1406.5033
75.	A. V. Shapovalov, A. Yu. Trifonov, Asymptotic solutions of the 1D nonlocal Fisher–KPP equation, 2014 , 35 pp., http://arxiv.org/abs/1409.3158v1, arXiv: 1409.3158 [math.AP]
76.	A. I. Breev, A. V. Shapovalov, “Yang–Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space”, Integrable systems and quantum symmetries (ISQS-2014) (Prague, June, 23-29, 2014), Journal of Physics: Conference Series, 563, 2014, 012004 , 15 pp.
77.	A. I. Breev, A. V. Shapovalov, “A spectrum of the Dirac operator with an external Yang-Mills gauge field on de Sitter space”, Proceedings of the International Conference “Quantum field theory and gravitation” (Tomsk, July 28-August 3 2014), Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta, 12(153), TGPU, Tomsk, 2014, 25-27

2013
78.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie. Chast III.1. Differentsialnoe ischislenie funktsii odnoi peremennoi, Natsionalnyi issledovatelskii Tomskii politekhnicheskii universitet, Tomsk, 2013 , 326 pp.
79.	A. L. Lisok, A. V. Shapovalov, A. Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross{Pitaevskii Equation”, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 9 (2013), 066 , 21 pp. http://dx.doi.org/10.3842/SIGMA.2013.066, arXiv: arXiv:1302.3326v2
80.	E. A. Levchenko, A. V. Shapovalov, and A. Yu. Trifonov, Pattern formation in terms of semiclassically limited distribution on lower-dimensional manifolds for nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, 2013 , 22 pp., arXiv: arXiv:1306.3765v1
81.	A. L. Lisok, A. V. Shapovalov, and A. Yu. Trifonov, Symmetry operators and intertwining operators for the nonlocal Gross–Pitaevskii equation, 2013 , 19 pp., arXiv: arXiv:1302.3326v1

2014
82.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Symmetry operators of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with a quadratic operator”, Russian Physics Journal, 56:12 (2014), 1415–1426

2013
83.	D. A. Vrazhnov, V. V. Nikolaev, A. V. Shapovalov, “Sravnitelnyi analiz metodov povysheniya ustoichivosti algoritmov slezheniya na video”, Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaya tekhnika i informatika, 2013, no. 4 (25), 23-31
84.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Computer Research and Modeling, 5:4 (2013), 543–558

2012
85.	E. A. Levchenko, A. V. Shapovalov, A. Yu. Trifonov, “Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation”, Journal of Mathematical Analysis and Applications (JMAA), 395:2 (2012), 716-726

2013
86.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Estimate of Accuracy of Solution of the Nonlocal Fisher–Kolomogorov–Petrovskii–Piskunov Equation”, Russian Physics Journal, 55:12 (2013), 1425-1433 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 47–53, December, 2012 http://link.springer.com/journal/11182/55/12/page/1

2012
87.	D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “On quality of object tracking algorithms”, Computer Research and Modeling, 4:2 (2012), 303–313
88.	A. V. Borisov, L. A. Krasnobaeva, A. V. Shapovalov, “Influence of diffusion and convection on the chemostat dynamics”, Computer Research and Modeling, 4:1 (2012), 121–129

2011
89.	E. Zamora Sillero, A. V. Shapovlov, “Equivalent Lagrangian densities and invariant collective coordinates equations”, J. Phys. A: Math. Theor., 44:6 (2011), 065204 (11 pp) http://iopscience.iop.org/1751-8121/44/6/065204
90.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Evolution of initial distributions with one and two centers in a two-dimensional model of the reaction-diffusion type with a nonlocal interaction of finite radius”, Russian Physics Journal, 54:1 (2011), 32–38 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 30–35, January, 2011. http://link.springer.com/journal/11182/54/1/page/1
91.	V. A. Aleutdinova, A. V. Borisov, V. É. Shaparev, A. V. Shapovalov, “Numerical simulation of the one-dimensional population dynamics with nonlocal competitive losses and convection”, Russian Physics Journal, 54:4 (2011), 479–484 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 76–80, April, 2011
92.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Nelokalnaya reaktsionno-diffuzionnaya dinamika formirovaniya krestoobraznykh dvumernykh dissipativnykh struktur”, Izvestiya Tomskogo politekhnicheskogo universiteta, 318:2 (2011), 48–52
93.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast II. .Analiticheskaya geometriya: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , 398 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
94.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast IV. .Ryady: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , 344 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
95.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast V. .Differentsialnye uravneniya: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
96.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Convection effect on two-dimensional dynamicsin the nonlocal reaction-diffusion model”, Computer Research and Modeling, 3:1 (2011), 55–61

2010
97.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Formirovanie dissipativnoi struktury v dvumernoi populyatsionnoi dinamike s nelokalnym vzaimodeistviem”, Izvestiya Tomskogo politekhnicheskogo universiteta, 316:2 (2010), 50-53
98.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Dvumernaya dinamika raspredelenii s odnim i dvumya tsentrami lokalizatsii v nelokalnoi reaktsionno-diffuzionnoi modeli”, Izvestiya Tomskogo politekhnicheskogo universiteta, 316:2 (2010), 54–58
99.	R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Sistema Einshteina-Erenfesta tipa (0,M) i asimptoticheskie resheniya mnogomernogo nelineinogo uravneniya Fokkera-Planka-Kolmogorova”, Kompyuternye issledovaniya i modelirovanie, 2:2 (2010), 151-160 http://crm.ics.org.ru/journal/issue/121/
100.	D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Simmetrii differentsialnykh uravnenii v zadachakh kompyuternogo zreniya”, Kompyuternye issledovaniya i modelirovanie, 2:4 (2010), 69-376 http://crm.ics.org.ru/journal/issue/125/
101.	E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie dlya odnomernogo dvukhkomponentnogo reaktsionno-diffuzionnogo uravneniya s nelokalnoi nelineinostyu”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2010, no. 2(61), 68-79 http://elibrary.ru/contents.asp?issueid=874155
102.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Vliyanie nelineinoi diffuzii na odnomernuyu reaktsionno-diffuzionnuyu dinamiku s nelokalnym samodeistviem”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2010, no. 2(61), 89–97 http://elibrary.ru/contents.asp?issueid=874155

2011
103.	A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii– Piskunov equation with nonlocal nonlinearity in polar coordinates”, Russian Physics Journal, 53:12 (2011), 1243-1253 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 21–29, December, 2010. http://link.springer.com/journal/11182/53/12/page/1

2010
104.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast I. Lineinaya algebra: Uchebnoe posobie, 2-e izd., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2010 , 310 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
105.	L. A. Krasnobaeva, A. V. Borisov, A. V. Shapovalov, Kompyuternye metody analiticheskikh vychislenii v prilozhenie k fizicheskim zadacham s ispolzovaniem matematicheskogo yazyka programmirovaniya Maple. [Elektronnyi resurs]: Laboratornyi praktikum, http://edu2.tsu.ru/eor/resourse/195/tpl/index.html, Institut distantsionnogo obrazovaniya TGU, Tomsk, 2010 , 52 pp.
106.	D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Symmetries of differential equations in computer vision applications”, Computer Research and Modeling, 2:4 (2010), 363–376
107.	R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “The Einstein-Ehrenfest system of (0, $M$)-type and asymptotical solutions of the multidimensional nonlinear Fokker-Planck-Kolmogorov equation”, Computer Research and Modeling, 2:2 (2010), 151–160
108.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Numerical modeling of population 2D-dynamics with nonlocal interaction”, Computer Research and Modeling, 2:1 (2010), 33–40

2009
109.	A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskie simmetrii uravneniya tipa Khartri s kvadratichnym operatorom”, Izvestiya Tomskogo politekhnicheskogo universiteta, 314:2 (2009), 66-71
110.	A. V. Borisov,R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Chislennoe modelirovanie odnomernoi populyatsionnoi dinamiki s nelokalnym vzaimodeistviem”, Izvestiya Tomskogo politekhnicheskogo universiteta, 315:2 (2009), 24–28
111.	V. A. Lyamkin, R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Sistema Einshteina-Erenfesta tipa (k, 1) dlya nelineinogo uravneniya Fokkera-Planka”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2009, no. 2(49), 26-37 http://elibrary.ru/contents.asp?issueid=650571
112.	A. Yu. Trifonov, A. V. Shapovalov, “The one-dimensional Fisher–Kolmogorov equation with a nonlocal nonlinearity in a semiclassical approximation”, Russian Physics Journal, 52:9 (2009), 899-911 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–23, September, 2009. http://link.springer.com/article/10.1007/s11182-010-9316-2
113.	E. I. Smirnova, A. Yu. Trifonov, A. V. Shapovalov, “Formalism of semiclassical asymptotics for a two-component Hartree-type equation”, Russian Physics Journal, 52:10 (2009), 1068-1076 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–66, October, 2009.
114.	L. A. Krasnobaeva, A. V. Shapovalov, “Modulation of the velocity of soliton-like perturbations for the sine–Gordon equation with external force and dissipation”, Russian Physics Journal, 52:12 (2009), 1331-1338 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 75–81, December, 2009.
115.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskie resheniya uravneniya Grossa–Pitaevskogo, lokalizovannye v okrestnosti okruzhnosti”, Kompyuternye issledovaniya i modelirovanie, 1:4 (2009), 359-365 http://crm.ics.org.ru/journal/issue/114/
116.	L. A. Krasnobaeva, A. V. Shapovalov, Solitony uravneniya sinus-Gordona, eds. d.f.-m.n. V. A. Kilin, Tomskii gosudarstvennyi universitet, Tomsk, 2009 , 192 pp., Uchebnoe posobie. Dopuscheno UMO po klassicheskomu universitetskomu obrazovaniyu v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu 010700 - Fizika
117.	V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. I. Lineinaya algebra: Uchebnoe posobie, eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2009 , 310 pp., Dopuscheno UMO po obrazovaniyu v oblasti prikladnoi matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po spetsialnosti 073000 “Prikladnaya matematika”
118.	L. A. Krasnobaeva, A. V. Shapovalov, “Kink motion by ac external force and dissipation”, Computer Research and Modeling, 1:3 (2009), 263–271
119.	A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Semiclassical asymptotics of nonlinear Fokker-Plank equation for distributions of asset returns”, Computer Research and Modeling, 1:1 (2009), 41–49
120.	A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical solutions localized in a neighborhood of a circle for the Gross-Pitaevskii equation”, Computer Research and Modeling, 1:4 (2009), 359–365

2008
121.	L. A. Krasnobaeva, A. V. Shapovalov, “Kink Velosity in Nonstationary External Fields for the Sine -Gordon Model with Allowance for Dissipation Effects”, Russian Physics Journal, 51:1 (2008), 89-98 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 77–84, January, 2008 http://link.springer.com/article/10.1007/s11182-008-9020-7
122.	L. A. Krasnobaeva, A. V. Shapovalov, “Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model”, Russian Physics Journal, 51:2 (2008), 158-167 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–51, February, 2008. http://link.springer.com/article/10.1007/s11182-008-9040-3
123.	A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Kvaziklassicheskoe priblizhenie dlya nelineninogo uravneniya Fokkera - Planka s kvadratichnoi diffuziei v modelyakh dokhodnostei aktivov”, “Matematika. Kompyuter. Obrazovanie”. Cbornik trudov XV mezhdunarodnoi konferentsii, Izhevsk: Nauchno-izdatelskii tsentr “Regulyarnaya i khaoticheskaya dinamika” (Moskovskaya oblast., g. Puschino, 8 yanvarya—2 fevralya 2008 goda), 1, eds. Pod obschei redaktsiei G.Yu. Riznichenko, Nauchno-izdatelskii tsentr “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2008, 181-189 http://www.mce.biophys.msu.ru/rus/archive/proceedings/mce15/part22253/doc21830/
124.	A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Nonlinear Fokker–Planck Equation in the Model of Asset Returns”, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4 (2008), 038 , 10 pp. http://www.emis.de/journals/SIGMA/2008/ $https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT={000267267800038$

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