Prikarpatskii Anatolii Karolevich

Publications in Math-Net.Ru

1. 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
2. Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
   
   SIGMA, 15 (2019), 079, 20 pp.
3. On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems
   
   SIGMA, 14 (2018), 023, 15 pp.
4. 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
5. The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models
   
   BJMP, 2:2 (2016),  105–196
6. On the classical Maxwell–Lorentz Electrodynamics, the electron inertia problem, and the feynman proper time paradigm
   
   Ukr. J. Phys., 61:3 (2016),  187–212
7. Maxwell–Lorentz electrodinamics revisited via the Lagrangian formalism and Feynman proper time paradigm
   
   Mathematics, 3:2 (2015),  190–257
8. Integrability of and differential–algebraic structures for spatially 1D hydrodynamical systems of Riemann type
   
   Chaos Solitons Fractals, 59 (2014),  59–81
9. A current algebra approach to the equilibrium classical statistical mechanics and its applications
   
   Cond. Matt. Phys., 16:2 (2013),  23702–13
10. The Maxwell electromagnetic equations and the Lorentz type force derivation-the Feynman approach legacy
    
    Internat. J. Theoret. Phys., 51:1 (2012),  237–245
11. On a Nonlocal Ostrovsky–Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability
    
    SIGMA, 6 (2010), 002, 13 pp.
12. The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry
    
    TMF, 160:2 (2009),  249–269
13. Verma modules over the quantum Lie algebra of currents on the circle
    
    Dokl. Akad. Nauk SSSR, 314:2 (1990),  268–272
14. 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
15. 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
16. 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
17. 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
18. An asymptotic method for constructing implectic and recursion operators of completely integrable dynamic systems
    
    Dokl. Akad. Nauk SSSR, 287:6 (1986),  1312–1317
19. A gradient algorithm for construction of criteria for integrability of nonlinear dynamical systems
    
    Dokl. Akad. Nauk SSSR, 287:4 (1986),  827–832
20. Complete integrability of the nonlinear ito and Benney–Kaup systems: Gradient algorithm and lax representation
    
    TMF, 67:3 (1986),  410–425
21. Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables
    
    TMF, 66:3 (1986),  463–480
22. The quantum Wigner operator and the method of Bogolyubov generating functionals in nonequilibrium statistical physics
    
    Dokl. Akad. Nauk SSSR, 285:6 (1985),  1365–1370
23. 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
24. Dynamical systems of Neumann type and their complete integrability
    
    Dokl. Akad. Nauk SSSR, 285:4 (1985),  853–857
25. Nonlinear model of Schrödinger type: Conservation laws, Hamiltonian structure, and complete integrability
    
    TMF, 65:2 (1985),  271–284
26. Inverse periodic problem for the discrete approximation of the Schrödinger nonlinear equation
    
    Dokl. Akad. Nauk SSSR, 262:5 (1982),  1103–1108
27. Discrete periodic problem for the modified nonlinear Korteweg–de Vries equation
    
    TMF, 50:1 (1982),  118–126
28. Discrete periodic problem for a modified nonlinear Korteweg-de Vries equation
    
    Dokl. Akad. Nauk SSSR, 258:3 (1981),  575–580
29. Almost periodic solutions of a modified nonlinear Schrödinger equation
    
    TMF, 47:3 (1981),  323–332
30. Geometrical structure and Bäcklund transformations of nonlinear evolution equations possessing a Lax representation
    
    TMF, 46:3 (1981),  382–393
31. On an analogue of the Bäcklund transformation for Riccati ordinary differential equations
    
    Dokl. Akad. Nauk SSSR, 253:2 (1980),  298–301
32. On Riccati equations integrable in quadratures
    
    Dokl. Akad. Nauk SSSR, 251:5 (1980),  1072–1077