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Prikarpatskii, Anatolii Karolevich
Statistics Math-Net.Ru
Total publications: 32
Scientific articles: 32
Presentations: 1

Number of views:
This page:3147
Abstract pages:7604
Full texts:2445
References:756
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https://www.mathnet.ru/eng/person23747
List of publications on Google Scholar
https://zbmath.org/authors/ai:prykarpatsky.anatoliy-karolevych
https://mathscinet.ams.org/mathscinet/MRAuthorID/196958

Publications in Math-Net.Ru Citations
2020
1. N. N. Bogolyubov (Jr.), D. Prorok, A. K. Prikarpatskii, “Integrability Aspects of the Current Algebra Representation and the Factorized Quantum Nonlinear Schrödinger Type Dynamical Systems”, Fiz. Elem. Chast. Atom. Yadra, 51:4 (2020),  468  mathnet  elib; Phys. Part. Nucl., 51:4 (2020), 434–442  isi  scopus 1
2019
2. Oksana Ye. Hentosh, Yarema A. Prikarpatsky, Denis Blackmore, Anatolij K. Prikarpatski, “Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics”, SIGMA, 15 (2019), 079, 20 pp.  mathnet  isi  scopus 4
2018
3. Anatolij K. Prykarpatski, “On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems”, SIGMA, 14 (2018), 023, 15 pp.  mathnet  isi  scopus 3
2017
4. A. K. Prikarpatski, N. N. Bogolyubov (Jr.), “The quantum charged particle self-interaction problem within the Fock many temporal and Feynman proper time paradigms”, Phys. Part. Nucl. Lett., 14:1 (2017),  87–101  mathnet  mathscinet  isi  scopus
2016
5. N. N. Bogolyubov (Jr.), D. Blackmore, A. K. Prikarpatskii, “The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models”, BJMP, 2:2 (2016),  105–196  mathnet
6. A. K. Prykarpatsky, N. N. Bogolubov, Jr., “On the classical Maxwell–Lorentz Electrodynamics, the electron inertia problem, and the feynman proper time paradigm”, Ukr. J. Phys., 61:3 (2016),  187–212  mathnet  mathscinet  isi  elib  scopus 3
2015
7. N. N. Bogolubov Jr., A. K. Prykarpatski, D. Blackmore, “Maxwell–Lorentz electrodinamics revisited via the Lagrangian formalism and Feynman proper time paradigm”, Mathematics, 3:2 (2015),  190–257  mathnet  zmath  isi 4
2014
8. D. Blackmore, Ya. A. Prikarpatsky, N. N. Bogolyubov (Jr.), A. K. Prikarpatski, “Integrability of and differential–algebraic structures for spatially 1D hydrodynamical systems of Riemann type”, Chaos Solitons Fractals, 59 (2014),  59–81  mathnet  mathscinet  zmath  isi  scopus 13
2013
9. N. N. Bogolyubov (Jr.), A. K. Prikarpatsky, “A current algebra approach to the equilibrium classical statistical mechanics and its applications”, Cond. Matt. Phys., 16:2 (2013),  23702–13  mathnet  isi  scopus 1
2012
10. A. K. Prikarpatsky, N. N. Bogolyubov (Jr.), “The Maxwell electromagnetic equations and the Lorentz type force derivation-the Feynman approach legacy”, Internat. J. Theoret. Phys., 51:1 (2012),  237–245  mathnet  zmath  isi  scopus 5
2010
11. Jołanta Golenia, Maxim V. Pavlov, Ziemowit Popowicz, Anatoliy K. Prykarpatsky, “On a Nonlocal Ostrovsky–Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability”, SIGMA, 6 (2010), 002, 13 pp.  mathnet  mathscinet  isi  scopus 21
2009
12. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, U. Taneri, “The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry”, TMF, 160:2 (2009),  249–269  mathnet  mathscinet; Theoret. and Math. Phys., 160:2 (2009), 1079–1095  isi 10
1990
13. N. N. Bogolyubov, I. V. Mykytyuk, A. K. Prikarpatskii, “Verma modules over the quantum Lie algebra of currents on the circle”, Dokl. Akad. Nauk SSSR, 314:2 (1990),  268–272  mathnet  mathscinet  zmath; Dokl. Math., 42:2 (1991), 424–428
14. A. K. Prikarpatskii, N. N. Bogolyubov, “A bilocal periodic problem for Sturm–Liouville and Dirac differential operators, and some applications in the theory of nonlinear dynamical systems”, Dokl. Akad. Nauk SSSR, 310:1 (1990),  29–32  mathnet  mathscinet  zmath; Dokl. Math., 41:1 (1990), 21–25
1988
15. A. K. Prikarpatskii, P. I. Kalenyuk, “Gibbs representations of the Lie algebra of currents, and the complete system of N. N. Bogolyubov quantum functional equations in equilibrium statistical mechanics”, Dokl. Akad. Nauk SSSR, 300:2 (1988),  346–349  mathnet  mathscinet; Dokl. Math., 33:5 (1988), 338–339
16. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics”, TMF, 75:1 (1988),  3–17  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 75:1 (1988), 329–339  isi 4
1986
17. A. M. Kurbatov, A. K. Prikarpatskii, S. V. Chelomei, “Complete integrability of dynamical systems associated with a problem of nonlinear vibrations of a longitudinally compressed beam”, Dokl. Akad. Nauk SSSR, 290:2 (1986),  304–308  mathnet  mathscinet  zmath
18. Yu. A. Mitropol'skii, A. K. Prikarpatskii, V. G. Samoilenko, “An asymptotic method for constructing implectic and recursion operators of completely integrable dynamic systems”, Dokl. Akad. Nauk SSSR, 287:6 (1986),  1312–1317  mathnet  mathscinet
19. A. K. Prikarpatskii, “A gradient algorithm for construction of criteria for integrability of nonlinear dynamical systems”, Dokl. Akad. Nauk SSSR, 287:4 (1986),  827–832  mathnet  mathscinet  zmath
20. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Complete integrability of the nonlinear ito and Benney–Kaup systems: Gradient algorithm and lax representation”, TMF, 67:3 (1986),  410–425  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 67:3 (1986), 586–596  isi 10
21. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables”, TMF, 66:3 (1986),  463–480  mathnet  mathscinet; Theoret. and Math. Phys., 66:3 (1986), 305–317  isi 2
1985
22. N. N. Bogolyubov, A. K. Prikarpatskii, “The quantum Wigner operator and the method of Bogolyubov generating functionals in nonequilibrium statistical physics”, Dokl. Akad. Nauk SSSR, 285:6 (1985),  1365–1370  mathnet  mathscinet
23. A. K. Prikarpatskii, “Bogoliubov generating functional method in the statistical physic and the transformation analog to the collective variables in a great canonical ensemble”, Dokl. Akad. Nauk SSSR, 285:5 (1985),  1096–1101  mathnet
24. N. N. Bogolyubov, A. K. Prikarpatskii, V. G. Samoilenko, “Dynamical systems of Neumann type and their complete integrability”, Dokl. Akad. Nauk SSSR, 285:4 (1985),  853–857  mathnet  mathscinet  zmath
25. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, A. M. Kurbatov, V. G. Samoilenko, “Nonlinear model of Schrödinger type: Conservation laws, Hamiltonian structure, and complete integrability”, TMF, 65:2 (1985),  271–284  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 65:2 (1985), 1154–1164  isi 5
1982
26. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Inverse periodic problem for the discrete approximation of the Schrödinger nonlinear equation”, Dokl. Akad. Nauk SSSR, 262:5 (1982),  1103–1108  mathnet 2
27. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, V. G. Samoilenko, “Discrete periodic problem for the modified nonlinear Korteweg–de Vries equation”, TMF, 50:1 (1982),  118–126  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 50:1 (1982), 75–81  isi 8
1981
28. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, V. G. Samoilenko, “Discrete periodic problem for a modified nonlinear Korteweg-de Vries equation”, Dokl. Akad. Nauk SSSR, 258:3 (1981),  575–580  mathnet  mathscinet
29. A. K. Prikarpatskii, “Almost periodic solutions of a modified nonlinear Schrödinger equation”, TMF, 47:3 (1981),  323–332  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 47:3 (1981), 487–493  isi 12
30. A. K. Prikarpatskii, “Geometrical structure and Bäcklund transformations of nonlinear evolution equations possessing a Lax representation”, TMF, 46:3 (1981),  382–393  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 46:3 (1981), 249–256  isi 8
1980
31. A. K. Prikarpatskii, “On an analogue of the Bäcklund transformation for Riccati ordinary differential equations”, Dokl. Akad. Nauk SSSR, 253:2 (1980),  298–301  mathnet  mathscinet  zmath 1
32. A. K. Prikarpatskii, “On Riccati equations integrable in quadratures”, Dokl. Akad. Nauk SSSR, 251:5 (1980),  1072–1077  mathnet  mathscinet  zmath 3

Presentations in Math-Net.Ru
1. On integrability of some Riemann type hydrodynamical systems and Dubrovin integrability classification of perturbed Korteweg-de Vries type equations
A. K. Prikarpatskii
Cohomological geometry of differential equations
March 24, 2021 19:20   

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