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Kapshai Valerii Nikolaevich

Publications in Math-Net.Ru

  1. Exact solutions of the two-dimensional Logunov–Tavkhelidze equation with the “delta-circle” potential for scattering states

    PFMT, 2025, no. 3(64),  67–72
  2. Numerical solution of the two-dimensional Logunov–Tavkhelidze equation for Gaussian potential in the relativistic configuration representation

    PFMT, 2025, no. 3(64),  56–61
  3. Exact solution of the quasipotential equation with the Coulomb potential in the momentum representation for coupled $s$-states with energy equal to zero

    PFMT, 2025, no. 2(63),  27–29
  4. Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$ in the relativistic configurational representation

    PFMT, 2023, no. 3(56),  12–15
  5. Solution of relativistic partial equations for scattering $d$-states

    PFMT, 2023, no. 1(54),  25–30
  6. Second-harmonic generation in the surface layer of a dielectric spheroidal particle: II. Analysis of the solution

    Optics and Spectroscopy, 130:7 (2022),  1082–1097
  7. Second-harmonic generation in the surface layer of a dielectric spheroidal particle: I. Analytical solution

    Optics and Spectroscopy, 130:7 (2022),  1068–1081
  8. Analysis of energy characteristics of the second-harmonic generation in long cylindrical dielectric particles

    PFMT, 2022, no. 4(53),  53–63
  9. Generation of sum-frequency waves in the surface layer of a spherical particle

    PFMT, 2022, no. 3(52),  22–27
  10. Approximate analytical solution of the Logunov–Tavkhelidze equation with a linear potential in the relativistic configurational representation

    PFMT, 2022, no. 2(51),  22–25
  11. Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation

    TMF, 211:3 (2022),  455–468
  12. Second harmonic–sum frequency generation in a thin spherical layer. IV. Optimization analysis

    Optics and Spectroscopy, 129:12 (2021),  1568–1582
  13. Second harmonic–sum frequency generation in a thin spherical layer. III. Properties of the solution

    Optics and Spectroscopy, 129:12 (2021),  1559–1567
  14. Second harmonic–sum frequency generation in a thin spherical layer. II. Analysis of directivity patterns

    Optics and Spectroscopy, 129:12 (2021),  1547–1558
  15. Second harmonic–sum frequency generation in a thin spherical layer. I. An analytical solution

    Optics and Spectroscopy, 129:12 (2021),  1537–1546
  16. Relativistic partial Green's functions of scattering states characterized by orbital quantum number $l=1$

    PFMT, 2021, no. 3(48),  7–13
  17. Some solutions of the dispersion equation for a moving biisotropic medium

    PFMT, 2021, no. 2(47),  35–38
  18. Reflection of a normally incident electromagnetic wave from a periodic biisotropic structure on a substrate

    PFMT, 2020, no. 2(43),  28–38
  19. Second-harmonic generation from a thin cylindrical layer: III. No-generation conditions

    Optics and Spectroscopy, 126:6 (2019),  740–747
  20. Second-harmonic generation from a thin cylindrical layer: II. Analysis of the solution

    Optics and Spectroscopy, 126:6 (2019),  732–739
  21. Second-harmonic generation from a thin cylindrical layer: I. Analytical solution

    Optics and Spectroscopy, 126:6 (2019),  724–731
  22. On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential

    PFMT, 2019, no. 4(41),  7–10
  23. Sum-frequency generation from a thin spherical layer: II. Analysis of solution

    Optics and Spectroscopy, 125:1 (2018),  71–78
  24. Sum-frequency generation from a thin spherical layer: I. Analytical solution

    Optics and Spectroscopy, 124:6 (2018),  795–803
  25. Ïîïðàâêà ê ñòàòüå “Ãåíåðàöèÿ ñóììàðíîé ÷àñòîòû îò òîíêîãî öèëèíäðè÷åñêîãî ñëîÿ” (òîì 124. N 1. 2017. C. 105–121)

    Optics and Spectroscopy, 124:5 (2018),  718
  26. Sum-frequency generation from a thin cylindrical layer

    Optics and Spectroscopy, 124:1 (2018),  105–121
  27. Relativistic scattering cross sections of a two-particle system in the case of interaction potentials containing a “barrier”

    PFMT, 2018, no. 1(34),  29–32
  28. Relativistic bound $s$-states problem for superposition of two potentials «$\delta$-sphere» type

    PFMT, 2017, no. 2(31),  15–19
  29. Relativistic scattering $s$-states problem for superposition of two potentials «$\delta$-sphere» type

    PFMT, 2015, no. 2(23),  7–12
  30. Covariant equations and resonance states of two-particle systems with $\delta$-function potentials

    PFMT, 2015, no. 1(22),  11–15
  31. Complex scaling method for two-particle equations in the momentum representation and resonance states

    PFMT, 2014, no. 3(20),  21–25
  32. Relativistic scattering problem for two-particle systems with one-boson exchange potentials

    PFMT, 2014, no. 2(19),  13–18
  33. Relativistic bound state problem for two-particle systems with energy dependent one boson exchange potential

    PFMT, 2013, no. 1(14),  24–26
  34. Transmission of plane electromagnetic waves trough a multilayer biisotropic structure

    PFMT, 2012, no. 4(13),  10–14
  35. Resonance states of relativistic systems and covariant two-particle equations

    PFMT, 2011, no. 4(9),  33–37
  36. Resonance structure of the scattering and extinction cross sections in the Mie problem for biisotropic sphere

    PFMT, 2011, no. 4(9),  28–32
  37. The stationary perturbation theory in case of a potential-series

    PFMT, 2011, no. 1(6),  29–35
  38. Identification of the influence of resonances on the cross section using Fredholm integral equation

    PFMT, 2010, no. 4(5),  10–17
  39. Scattering of electromagnetic waves on biisotropic sphere in biisotropic medium

    PFMT, 2010, no. 3(4),  7–21
  40. Three-dimensional covariant one-time equations for a system of $n$ spinor particles

    TMF, 101:1 (1994),  69–84
  41. Exact solutions of a class of quasipotential equations for a superposition of one-boson exchange quasipotentials

    TMF, 82:2 (1990),  188–198
  42. Dependence of the quasipotential on the total energy of a two-particle system

    TMF, 69:3 (1986),  400–410
  43. Exact solution of quasipotential equations of general form with chromodynamic interaction

    TMF, 69:1 (1986),  55–68
  44. On a class of exact solutions of quasipotential equations

    TMF, 55:3 (1983),  349–360
  45. Exact solutions of quasipotential equations for the Coulomb potential and a linear confining potential

    TMF, 55:2 (1983),  236–245
  46. Covariant two-particle wave functions for model quasipotentials that admit exact solutions. II. Solutions in the relativistic configuration representation

    TMF, 55:1 (1983),  26–38
  47. Covariant two-particle wave functions for model quasipotentials that admit exact solutions. I. Solutions in momentum space

    TMF, 54:3 (1983),  406–415
  48. Structure functions of pseudoscalar mesons in a composite model with chromodynamic interaction

    TMF, 53:3 (1982),  388–398
  49. Exact solution of covariant two-particle one-time equation with superposition of one-boson exchange quasipotentials

    TMF, 53:1 (1982),  32–42

© Steklov Math. Inst. of RAS, 2026