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Valovik Dmitry Viktorovich

Publications in Math-Net.Ru

  1. Existence of solutions of a nonlinear eigenvalue problem and their properties

    Mat. Sb., 215:1 (2024),  59–81
  2. On a nonstandard perturbation method for proving the existence of nonlinearizable solutions in a nonlinear eigenvalue problem arising in waveguide theory

    Zh. Vychisl. Mat. Mat. Fiz., 64:10 (2024),  1949–1965
  3. Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide I: TE-TE waves

    Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021),  108–123
  4. Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176 (2020),  34–49
  5. On the integral characteristic function of the Sturm-Liouville problem

    Mat. Sb., 211:11 (2020),  41–53
  6. Propagation of electromagnetic waves in an open planar dielectric waveguide filled with a nonlinear medium II: TM waves

    Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020),  429–450
  7. Multiparameter eigenvalue problems and their applications in electrodynamics

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 172 (2019),  9–29
  8. Propagation of electromagnetic waves in an open planar dielectric waveguide filled with an nonlinear medium I: TE waves

    Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019),  838–858
  9. On the existence of an infinite number of eigenvalues in one nonlinear problem of waveguide theory

    Zh. Vychisl. Mat. Mat. Fiz., 58:10 (2018),  1656–1665
  10. A note on hybrid waves in plane layered waveguiding structures

    University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 3,  3–14
  11. The spectral properties of some nonlinear operators of Sturm-Liouville type

    Mat. Sb., 208:9 (2017),  26–41
  12. Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide

    Zh. Vychisl. Mat. Mat. Fiz., 57:8 (2017),  1304–1320
  13. On one approach to the problem of polarized electromagnetic waves diffraction on a dielectric layer filled with a nonlinear medium

    University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 4,  28–37
  14. Existence and unicity of the solution of the diffraction problem for an electromagnetic wave on a system of non-intersecting bodies and screens

    University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 1,  89–97
  15. On the problem of propagation of nonlinear coupled TE–TM waves in a layer

    Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014),  504–518
  16. A nonlinear transmission eigenvalue problem that describes electromagnetic าล wave propagation in a plane inhomogeneous nonlinear dielectric waveguide

    University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 2,  50–63
  17. Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides

    Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013),  1150–1161
  18. The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013),  74–89
  19. The problem of diffraction of electromagnetic TE waves on a nonlinear layer

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 4,  73–83
  20. Propagation of coupled electromagnetic TE and TM waves in a plane layer with Kerr nonlinearity

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 4,  21–48
  21. Numerical solution of the problem of propagation of electromagnetic TM waves in a circular dielectric waveguide filled with a nonlinear medium

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 3,  29–37
  22. On the propagation of electromagnetic waves in cylindrical inhomogeneous dielectric waveguides filled with a nonlinear medium

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 3,  3–16
  23. Coupling problem for electromagnetic TE waves propagating in a flat two-layer nonlinear dielectric waveguide

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 2,  43–49
  24. Numerical method in the problem of propagation of electromagnetic TE waves in a two-layer nonlinear waveguide structure

    University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1,  66–74
  25. Propagation of TM waves in a layer with arbitrary nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 51:9 (2011),  1729–1739
  26. Collocation method for solving the electric field equation

    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 4,  89–100
  27. Propagation of TM-polarized electromagnetic waves in a dielectric layer of a nonlinear metamaterial

    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 3,  71–87
  28. The problem of propagation of electromagnetic waves in a layer with arbitrary nonlinearity (II. TM waves)

    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 2,  54–65
  29. Dispersion equations in the problem of electromagnetic wave propagation in a linear layer and metamaterials

    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 1,  28–42
  30. The problem of propagation of electromagnetic waves in a layer with arbitrary nonlinearity (I. TE are the waves)

    University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 1,  18–27
  31. The method of pseudodifferential operators for the study of a volumetric singular integral equation of an electric field

    University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 4,  70–84
  32. Analytical continuation of the Green's function for the equation Helmholtz in the layer

    University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 2,  83–90
  33. A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer

    Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10,  70–74
  34. On the existence of solutions to the nonlinear boundary value eigenvalue problem for TM-polarized electromagnetic waves

    University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 2,  86–94
  35. Propagation of TM waves in a Kerr nonlinear layer

    Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008),  2186–2194

© Steklov Math. Inst. of RAS, 2026