Leonid Nizhnik's Home Page

Back to Leonid Nizhnik's homepage

SELECTED PUBLICATIONS

Leonid NIZHNIK

1. Die Programmierung von Tabellen fur optimale Methoden der statistischen Qualitatskontrolle, (with Korolyuk, V.S. and Yushchenko, E.L.), Text.Article, Vopr. Vychisl. Mat. Tekhn. No.3, 9-17 (1958).

2. On the spectrum of general differential operators. Dokl. Akad. Nauk SSSR 124 (1959), 517- 519.

3. The scattering problem for non-stationary perturbations. Dokl. Akad. Nauk SSSR 132, 40-43 (Russian); translated as Soviet Math. Dokl. 1 (1960), 478-481.

4. Problem of dispersion for a Schrodinger equation. (Russian) Ukrain. Mat. Zh. 12 (1960)209-212.

5. A problem in inelastic scattering. Dokl. Akad. Nauk SSSR 140 (1961) 533-535.

6. Spectral Properties of Some Differential Operators and Scattering Problems, PhD thesis, Kiev,1961.

7. A priori inequalities for certain differential operators with continuous coefficients. (Russian) Ukrain. Mat. Zh. 14 (1962) 426-431.

8. Spectral structure and the self-adjointness of perturbations of differential operators with constant coefficients. (Russian) Ukrain. Mat. Zh. 15 (1963) 385-399.

9. The spectrum properties of self-adjoint partial differential operators which are close to the operators with constant coefficients. 1963 Outlines Joint Sympos. Partial Differential Equations (Novosibirsk, 1963) pp. 195-199 Acad. Sci. USSR Siberian Branch, Moscow.

10. Calculation of additional losses in transformers tanks, (with Berezovsky, A. and Kravchenko, A.), Elektrichestvo, n 9, (1966), 1-7.

11. A correctly posed problem without initial data for the wave equation. (Russian) Ukrain. Mat. Zh. 20 (1968 ) 802-813.

12. Analytic continuation of the resolvent of a selfadjoint operator in terms of a continuous spectrum, (with Djuzhenkova, L.) (Russian) Ukrain. Mat. Zh. 20 (1968) 759-765.

13. Mathematical models of hysteresis, (with Beresovsky, A.) (Russian) Proceedings of V Int. conference on nonlinear oscillations, Kiev, Institute of Mathematics, 1970, 68-71.

14. Calculations of electro-magnetic fields and additional losses in active zone turbo-generators, (with Berezovsky, A. and Kravchenko, A.), Elektrichestvo, n 11, (1970), 6-11.

15. An inverse problem of nonstationary scattering, Soviet Math. Dokl., 12, 1, 306-310, (1971).

16. Cybernetics and computer technology. No. 11: Methods of calculating electromagnetic fields on computers ``Naukova Dumka'', Kiev, 1971. 143 pp.

17. Boundary value problems of mathematical physics. Edited by Ju. O. Mitropolski. Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1971. 367 pp.

18. The nonstationary scattering problem for the Dirac equations on the half-axis. (Russian) Boundary value problems of mathematical physics (Russian), pp. 303-313. Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1971.

19. The inverse nonstationary scattering problem for a hyperbolic system of equations. (Russian) Linear and nonlinear boundary value problems (Russian), pp. 205-210. Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1971.

20. Nonstationary inverse scattering problem for the Dirac equation, Ukrain. Math. J., 24, 1, 110-113, (1972).

21. Mathematics and progress in science and technology. Proceedings of a Republican Scientific Conference (Kiev, January 23-25, 1973). Edited by Ju. O. Mitropol'ski. Izdat. ``Naukova Dumka'', Kiev, 1973. 341 pp.

22. The inverse nonstationary scattering problem, Kiev, Naukova Dumka, pp. 182, (1973), (in Russian).

23. An inverse scattering problem on the semi-axis with a nonselfadjoint potential matrix. (Russian), (with Fam Loi Vu), Ukrain. Mat. Zh. 26 (1974), 469-486.

24. Rectangular conductive wedge in travelling electromagnetic field, (with Mayergoyz, I.) Zh. Tech. Phys., 44, 10 (1974), 2058-2068.

25. Spectral theory of operators and infinite-dimensional analysis. Edited by Ju. M. Berezanski, M. L. Gorbachuk and L. P. Nizhnik. Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1976. 148 pp.

26. The inverse nonstationary scattering problem for a hyperbolic system of equations,
(with Tarasov, V.G.), (Russian) .Dokl. Akad. Nauk SSSR 233 (1977), no. 3, 300-303, translated Soviet Math. Dokl. 18, 2, 397-401, (1977).

27. Nonstationary Inverse Scattering Problem, Doctor thesis, Kiev, 1977.

28. Electrodynamic computations in electrical engineering, (with Kravchenko, A.N.) (Russian). Kiev.: "Technika", 1977, 184pp.

29. An inverse problem of scattering for a one-velocity transfer equation, (with Tarasov V.G.), (Russian) Dokl. Akad. Nauk SSSR 242 (1978), no. 6, 1307-1310, translated Soviet Phys. Dokl. 23, 10, 728-730, (1978).

30. The 12th Mathematical School. (Russian) Methods of functional analysis in problems of mathematical physics (Russian), (with Romanenko, R.), pp. 5-7, 179, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1978.

31. An inverse scattering problem on a nonstationary potential in three-dimensional space. (Russian) Methods of functional analysis in problems of mathematical physics (Russian), pp. 38-62, 181, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1978.

32. Numerically-analytical methods of transformer electromagnetic fields calculations,
(with Ivankov, V.F.) in Int. Symposium on Electrodynamics Forces and Losses in Transformers. Lodz, 1979, pp.330-333.

33. Integration of multidimensional nonlinear equations by the inverse problem method, Dokl. Akad. Nauk SSSR, 254, N 2, 332-335, (1980).

34. Inverse scattering problem for a transport equation that is discrete in directions. (with Tarasov, V.) (Russian) Ukrain. Mat. Zh. 32 (1980), no. 5, 678-683.

35. Conditional stability of an inverse nonstationary scattering problem, (with Romanenko, R.) (Russian) Ukrain. Mat. Zh. 33 (1981), no. 5, 694-696.

36. An inverse scattering problem for a functional-differential equation. (Russian) Direct and inverse problems of scattering theory, pp. 55-61, 149, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1981.

37. An inverse stationary scattering problem for a hyperbolic system of equations. (Russian) Direct and inverse problems of scattering theory, (with Tarasov, V.) , pp. 61-76, 149, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1981.

38. Boundary value problems for the heat equation with a time derivative under conjugation conditions, (with Taraborkin, L.) (Russian) Ukrain. Mat. Zh. 34 (1982), no. 1, 121-126.

39. Integration of the nonlinear Schrodinger equation in two spatial dimensions by the inverse scattering method (with Pochinayko, M.D.), Funct. Analys. and Appl. 16, N 180-82, (1982).

40. The regularization method in factorization problems, (with Rozanov, R. A.), (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 22 (1982), no. 3, 540-547.

41. An inverse nonstationary scattering problem for a system of second-order equations,
(with Fam Loi Vu), Ukrain. Mat. Zh. 34 (1982), no. 6, 718-724.

42. An inverse scattering problem on the whole axis for a system of second-order ordinary differential equations, (with Fam Loi Vu), (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1983, no. 23, 16pp.

43. The inverse scattering problem for a difference analogue of a two-dimensional system of Dirac equations, (with Goncharenko, Yu. V.) (Russian) The spectral theory of operators in problems of mathematical physics, 58-71, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1983.

44. The inverse scattering problem for a system of Dirac equations in characteristic variables, (with Pochinaiko, M. D. and Tarasov, V. G.) (Russian) The spectral theory of operators in problems of mathematical physics, 72-93, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1983.

45. Nonlinear problems of heat conduction with a time derivative in the boundary condition and in conjugation conditions, (with Taraborkin, L.) (Russian) General theory of boundary value problems, 156-159, "Naukova Dumka", Kiev, 1983.

46. Multidimensional inverse scattering problems. (Russian) Ill-posed problems of mathematical physics and analysis, 101-106, 258, "Nauka" Sibirsk. Otdel., Novosibirsk, 1984.

47. Integrating multidimensional nonlinear equations by the inverse scattering method. Nonlinear and turbulent processes in physics, Vol. 3 (Kiev, 1983), 1525-1528, Harwood Academic Publ., Chur, 1984.

48. Integration of the nonlinear two-dimensional Toda lattice by the inverse scattering method, (with Goncharenko, Yu.V.) (Russian) Differential-difference equations and problems of mathematical physics (Russian), 25-28, 132, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1984.

49. Spatially two-dimensional nonlinear Schrodinger equation as an integrable Hamiltonian, (with Pochinaiko, M.D.) (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1985, no. 24, 22 pp.

50. Methods for determining a quasistationary magnetic field in the presence of massive conducting bodies, (with Kravchenko, A. N. and Ivankov, V. F.) (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1985, no. 80, 14 pp.

51. Eddy currents and losses in the transformer tank cover induced by the field of heavy current taps, (with Bereza, V., Furman, Ya. and Ivankov,V.), Int. Symposium on Electromagnetic Fields in Electrical Engineering, Warsaw, 1985, 245-248.

52. An inverse scattering problem for a two-dimensional difference equation with a four-point pattern,(with Goncharenko, Yu. V.) (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1985, no. 81, 36 pp.

53. The inverse scattering problem for an integro-differential equation, (with Tarasov, V.G.) (Russian) Direct and inverse problems of the spectral theory of differential operators (Russian), 71-92, viii, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1985.

54. An inverse scattering problem for a difference equation in a half-plane. (Russian) The spectral theory of operator-differential equations (Russian), 80-88, v, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1986.

55. Investigation of the Cauchy problem for the two-space-dimensional nonlinear Schrodinger equation by the method of the inverse scattering problem, (with Pochinaiko, M. D.) (Russian) The spectral theory of operator-differential equations (Russian), 89-98, v, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1986.

56. Calculation of the quasi-stationary magnetic field in the region surrounded by the conducting solid medium using the eigenfunctions method,(with Kravchenko, A.) in Prace Institutu Elektrotechniki, Vol. 147. Warsaw, 1987, 119-146.

57. The inverse scattering problems for hyperbolic equations and their application to nonlinear integrable systems, Rep. Math. Phys., 26, N 2, 261-283, (1988).

58. Spectral analysis of the two-dimensional Dirac operator, (with Amerova, E.I.) (Russian) Boundary value problems for differential equations (Russian), 4-5, i, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1988.

59. An inverse nonstationary scattering problem for a hyperbolic system of three first-order equations on the half-axis, (with Iskenderov, N. Sh.) (Russian) Ukrain. Mat. Zh. 42 (1990), no. 7, 931-938; translation in Ukrainian Math. J. 42 (1990), no. 7, 825-832 (1991).

60. Selfadjoint operators generated by nonhomogeneous elliptic problems with discontinuous boundary conditions and conjugation conditions, (with Taraborkin, L. A.)(Russian) Ukrain. Mat. Zh. 43 (1991), no. 3, 374-381; translation in Ukrainian Math. J. 43 (1991), no. 3, 338-345.

61. The inverse scattering problem for an integrodifferential equation, (with Tarasov, V. G.) [translation of Direct and inverse problems of the spectral theory of differential operators (Russian), 71-92, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1985; Selected translations. Selecta Math. Soviet. 10 (1991), no. 3, 219-236.

62. Inverse scattering problems for hyperbolic equations, Kiev, Naukova dumka, (1991), (in Russian). 232 pp.

63. Conditional stability of the inverse scattering problem for the Dirac system, (with Romanenko, R.) (Russian) Applications of the methods of functional analysis in mathematical physics (Russian), 78-88, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1991.

64. Regularization method in nonstationary inverse scattering problem. Ill-posed problems in natural sciences, (with Romanenko, R.)(Moscow, 1991), 563-567, VSP, Utrecht, 1992.

65. A multidimensional inverse scattering problem for a system of first-order partial differential equations, (with Tarasov, V. G.) (Russian) Boundary value problems for differential equations (Russian), 84-93, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1992.

66. Conditional stability of inverse scattering problem for two-dimensional Dirac system, (with Romanenko, R. V.) Methods of functional analysis in problems of mathematical physics, 87-96, Acad. Sci. Ukraine, Inst. Math., Kiev, 1992.

67. An evolution problem for harmonic functions in a domain with a thin inclusion, (with Taraborkin, L.) (Russian) Dopov./Dokl. Akad. Nauk Ukraini 1994, no. 1, 13-16.

68. Spectral properties of two-dimensional nonstationary Dirac operator, (with Amerova, E.), (Russian) Ukrain. Mat. Zh. 47 (1995), no. 5, 593-599; translation in Ukrainian Math. J. 47 (1995), no. 5, 686-693 (1996).

69. Inverse scattering problems for hyperbolic equations and their applications, in Algebraic and Geometric Methods in Mathematical Physics, Proceedings of the International Conference, Ukraine, Crimea, Kaciveli, 1993.(A. Boutet de Monvel and V. Marchenko, Eds). Kluwer Academic Publishers, Dordrecht, 1996, pp.439-441.

70. Inverse scattering problem for the wave equations and its applications, Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, 1995. (J. Gottlieb and P. DuChateau, Eds). Water Sci. Technol. Libr., 23, Kluwer Academic Publishers, Dordrecht, 1996, pp. 233-238.

71. On One Point Interaction in Quantum Mechanics Ukrain. Mat. Zh. 49, N 11, (1997), pp.1557-1560. translation in Ukrainian Math. J. 49 (1997), no. 11, 1752-1755 (1998).

72. Representations of double commutator by matrix-differential operators, (with Turowska, L. ) Methods Funct. Anal. Topology 3, N 3 (1997), pp. 75-80.

73. Scattering Problem for Multidimensional System of the First Order Partial Differential Equations, (with Tarasov, V.G.), Ukrain. Mat. Zh. 51, N 8 (1999) , pp. 1065-1076. translation in Ukr. Math. J, 51 (1999), no. 8, 1201-1213 (2000).

74. Direct and Inverse Scattering Problems for Multidimensional System of First-Order Partial Differential Equations, (with Tarasov, V.G.), Methods Funct. Anal. Topology, 5 , N 2 (1999), pp. 44-82.

75. Inverse scattering problem for the multidimensional first-order hyperbolic system. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), 523-527, SIAM, Philadelphia, PA, 2000.

76. Approximation of General Zero-Range Potentials, (with Albeverio, S.) Ukrain. Mat. Zh. 52 (2000), no. 5, 582-589; translation in Ukrainian Math. J. 52 (2000), no. 5, 664-672 (2001).

77. On rank one singular perturbations of selfadjoint operators. Methods Funct. Anal. Topology 7 (2001), no. 3, 54-66.

78. Boundary value problems with singular conditions on boundary components of small dimensions. Methods Funct. Anal. Topology, 1, (2001), 76-81.

79. Stable stationary solutions in reaction-diffusion systems consisting of a 1-D array of bistable cells, (with Hasler, M. and Nizhnik, I.), Int. J. of Bifurcation and Chaos 2 , (2002), 261-279.

80. On approximations of rank one H_(-2)-perturbations, (with Albeverio, S., Koshmanenko,V., and Kurasov, P.), Proc. Amer. Math. Soc. 5, (2002), 1443-1452.

81. A generalized sum of quadratic forms, (with Brasche, J.) , Methods of Funct. Anal. Topology, n3 (2002), 13-19.

82. Schrodinger operator with δ ′-interaction. J. Funct. Anal. Appl., Vol. 37, 1, (2003), 72-74.

83. On the number of negative eigenvalues of a one-dimensional Schrodinger operator with point interaction, (with Albeverio, S.), Lett. Math. Phys., 65, (2003), 27-35.

84. Schrodinger operators with a number of negative eigenvalues equal to the number of point interactions, (with Albeverio, S.), Methods of Funct. Anal. Topology, 9, n 4, (2003), 273-286.

85. A Schrodinger operator with δ ′-interaction on a Cantor set and Krein-Feller operators,
(with Albeverio S.), Preprint no99, Universitat Bonn, SFB611, Mathematische Nachrichten 279, No. 5-6, (2006), 467-476.

86. Inverse scattering problem for a Dirac system with nonstationary point interactions,
(with Albeverio, S. and Tarasov, V.), Preprint no71, Universitat Bonn, SFB611, Inverse Problems, 20,(2004), 799-813.

87. Traveling avalanche waves in spatially discrete bistable reaction- diffusion systems,
(with Hasler, M. and Nizhnik, I.), Preprint 03- 05-115 BiBoS Universitat Bielefeld.

88. A Schrodinger operator with point interactions on the Sobolev spaces, (with Albeverio, S.),
Lett. Math. Phys. 70, (2004), 185-194.

89. Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries, (with Albeverio, S., Galperin, G. and Nizhnik, I.) Preprint 04- 08-154 BiBoS Universitat Bielefeld, (2004), Regular and Chaotic Dynamics, 10 (3), (2005), 285-306.

90. Generalized translation operators and hypergroups constructed from self-adjoint differential operators, (with Kosyak, A.), tranl in Ukrainian Math. J., 57, N5, (2005), 782 - 793.

91. One-dimensional Schrodinger operators with point interactions on Sobolev spaces,
J. Funct. Anal. Appl. 40, n. 2, (2006), 74 - 79.

92. Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces, (with Albeverio, S., Kuzhel, S.), Ukrain. Math. J., Vol 59, 6, 723-743.

93. Finite Rank Self-Adjoint Perturbations, (with Kuzhel, S.), Methods Funct. Anal. Topology, 12, n.3, 243-253.

94. Schrodinger operators with nonlocal point interactions, (with Albeverio, S.), J.Math. Anal. Appl. 332 (2007) 884-895.

Back to Leonid Nizhnik's homepage