Із симетрією в житті та математиці
До 75-річчя члена-кореспондента НАН України А.Г. Нікітіна
DOI:
https://doi.org/10.15407/visn2020.12.087Анотація
25 грудня виповнюється 75 років відомому українському фахівцю в галузі математичної фізики, лауреату Державної премії України в галузі науки і техніки (2001) та премії імені М.М. Крилова НАН України (2010), завідувачу відділу математичної фізики Інституту математики НАН України, доктору фізико-математичних наук (1987), професору (2001), члену-кореспонденту НАН України (2009) Анатолію Глібовичу Нікітіну.
Посилання
Fushchich W.I., Grishchenko A.L., Nikitin A.G. On relativistic equations of motion without “redundant” components. Theor. Math. Phys. 1971. 8(2): 766–775. DOI: https://doi.org/10.1007/BF01037997
Fushchich W.I., Nikitin A.G. Symmetries of Maxwell’s equations. Dordrecht: D. Reidel, 1987.
Fushchich W.I., Nikitin A.G. Symmetries of equations of quantum mechanics. N.Y.: Allerton Press, 1994.
Nikitin A.G. (ed.) Symmetry and Integrability of Equations of Mathematical Physics (dedicated to the 70th anniversary of Professor W.I. Fushchych). Transactions of Institute of Mathematics of NAS of Ukraine. 2006. 3(2): 5–8. (in Ukrainian). http://trim.imath.kiev.ua/index.php/trim/issue/view/20
Nikitin A.G., Fushchich W.I. Equations of motion for particles of arbitrary spin invariant under the Galilei group. Theor. Math. Phys. 1980. 44(1): 584–592. DOI: https://doi.org/10.1007/BF01038008
Fushchich W.I., Nikitin A.G. Nonrelativistic equations of motion for particles with arbitrary spin. Sov. J. Particles Nucl. 1981. 12: 1157–1219.
de Montigny M., Niederle J. Nikitin A.G. Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions. J. Phys. A: Math. Gen. 2006. 39(29):9365–9385. https://doi.org/10.1088/0305-4470/39/29/026
Fushchich W.I., Nikitin A.G. Poincare-invariant equations of motion for particles of arbitrary spin. Sov. J. Particles Nucl. 1978. 9: 501–553.
Niederle J., Nikitin A.G. Relativistic wave equations for interacting, massive particles with arbitrary half-integer spins. Phys. Rev. 2001. D 64: 125013–125024. DOI: https://doi.org/10.1103/PhysRevD.64.125013
Niederle J., Nikitin A.G. Relativistic Coulomb problem for particles with arbitrary half-integer spin. J. Phys. A: Math. Gen. 2006. 39(34): 10931–10944. DOI: https://doi.org/10.1088/0305-4470/39/34/023
Fushchich W.I., Nikitin A.G. New invariance algebras of relativistic equations for massless particles. J. Phys. A: Math. Gen. 1979. 12(6): 747–757. https://doi.org/10.1088/0305-4470/12/6/005
Fushchych W.I., Nikitin A.G. The complete set of conservation laws for the electromagnetic field. J. Phys. A: Math. Gen. 1992. 25(5): L231–L233. DOI: https://doi.org/10.1088/0305-4470/25/5/004
Beckers J., Debergh N., Nikitin A.G. On supersymmetries in nonrelativistic quantum mechanics. J. Math. Phys. 1992. 33(1): 152–160. DOI: https://doi.org/10.1063/1.529954
Beckers J., Debergh N., Nikitin A.G. On parasupersymmetries and relativistic description for spin one particles. I. The free particle context. Fort. Phys. 1995. 43(1): 67–80. DOI: https://doi.org/10.1002/prop.2190430104
Beckers J., Debergh N., Nikitin A.G. Reducibility of supersymmetric quantum mechanics. Int. J. Theor. Phys. 1997. 36: 1991–2003. DOI: https://doi.org/10.1007/BF02435955
Nikitin A.G., Wiltshire R.J. Symmetries of systems of nonlinear reaction-diffusion equations. Proc. of Inst. of Mathematics of the Nat. Acad. Sci. of the Ukraine. 2000. 30 (Part 1): 47–59. https://www.imath.kiev.ua/~symmetry/Symmetry99/art4.pdf
Nikitin A.G., Wiltshire R.J. Systems of reaction diffusion equations and their symmetry properties. J. Math. Phys. 2001. 42(4): 1667–1688. DOI: https://doi.org/10.1063/1.1331318
Nikitin A.G. Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. I. Generalized Ginsburg–Landau equations. J. Math. Anal. Appl. 2006. 324(1): 615–628. DOI: https://doi.org/10.1016/j.jmaa.2005.12.022
Nikitin A.G. Group classification of systems of non-linear reaction-diffusion equations with triangular diffusion matrix. Ukr. Math. J. 2007. 59: 395–411. DOI: https://doi.org/10.1007/s11253-007-0028-x
Nikitin A.G., Spichak S.V., Vedula Yu.S., Naumovets A.G. Symmetries and modelling functions for diffusion processes. J. Phys. D: Appl. Phys. 2009. 42(5): 055301. DOI: https://doi.org/10.1088/0022-3727/42/5/055301
Nikitin A.G., Kuriksha O. Symmetries of field equations of axion electrodynamics. Phys. Rev. D. 2012. 86: 025010. DOI: https://doi.org/10.1103/PhysRevD.86.025010
Nikitin A.G., Karadzhov Yu. Matrix superpotentials. J. Phys. A: Math. Theor. 2011. 44(30): 305204. DOI: https://doi.org/10.1088/1751-8113/44/30/305204
Nikitin A.G. Matrix superpotentials and superintegrable systems for arbitrary spin. J. Phys. A: Math. Theor. 2012. 45: 225205. DOI: https://doi.org/10.1088/1751-8113/45/22/225205
Nikitin A.G. Laplace–Runge–Lenz vector for arbitrary spin. 2013. J. Math. Phys. 54: 123506. DOI: https://doi.org/10.1063/1.4843435
Nikitin A.G. New exactly solvable systems with Fock symmetry. J. Phys. A: Math. Theor. 2012. 45: 485204. DOI: https://doi.org/10.1088/1751-8113/45/48/485204
Nikitin A.G. Superintegrability and supersymmetry of Schrödinger–Pauli equations for neutral particles. J. Math. Phys. 2012. 53(12): 122103. DOI: https://doi.org/10.1063/1.4768464
Nikitin A.G. Superintegrable and shape invariant systems with position dependent mass. J. Phys. A: Math. Theor. 2015. 48: 335201. DOI: https://doi.org/10.1088/1751-8113/48/33/335201
Nikitin A.G. Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses. J. Math. Phys. 2017. 58(8): 083508. DOI: https://doi.org/10.1063/1.4986171
Nikitin A.G. Symmetries of Schrödinger equation with scalar and vector potentials. J. Phys. A: Math. Theor. 2020. 53: 455202. DOI: https://doi.org/10.1088/1751-8121/abb956
