All Stories

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

    Article • Математический сборник, December 2023, Steklov Mathematical Institute

    Dmitry V. Valovik

  2. Electromagnetic Guided Wave in Goubau Line with Graphene Covering: TE Case

    Article • Photonics, October 2023, MDPI AG

    Dmitry V. Valovik

  3. Maxwell’s Equations with Nonlinear Inhomogeneous Constitutive Relation: Guided Waves in a Film Filled with Inhomogeneous Kerr Medium

    Article • SIAM Journal on Applied Mathematics, April 2023, Society for Industrial & Applied Mathematics (SIAM)

    Dmitry V. Valovik

  4. Nonclassical perturbation approach to a nonlinear multiparameter eigenvalue problem arising in electromagnetics

    Article • Mathematical Methods in the Applied Sciences, April 2023, Wiley

    Dmitry V. Valovik

  5. Transverse Electric Guided Wave Propagation in a Plane Waveguide with Kerr Nonlinearity and Perturbed Inhomogeneity in the Permittivity Function

    Article • Photonics, March 2023, MDPI AG

    Dmitry V. Valovik

  6. On a Different Vision of Kerr Law in Nonlinear Optical Waveguide Theory

    Article • Photonics, November 2022, MDPI AG

    Dmitry V. Valovik

  7. Theory of nonlinear transverse-magnetic guided waves in a plane waveguide filled with nonhomogeneous nonlinear medium

    Article • Waves in Random and Complex Media, July 2022, Taylor & Francis

    Dmitry V. Valovik

  8. Nonlinearizable solutions in an eigenvalue problem for Maxwell's equations with nonhomogeneous nonlinear permittivity in a layer

    Article • Studies in Applied Mathematics, June 2022, Wiley

    Dmitry V. Valovik

  9. Integral Characteristic Function of a Nonlinear Sturm–Liouville Problem

    Article • Differential Equations, December 2021, Pleiades Publishing Ltd

    Dmitry V. Valovik

  10. Perturbation Method in the Theory of Propagation of Two-Frequency Electromagnetic Waves in a Nonlinear Waveguide I: TE-TE Waves

    Article • Computational Mathematics and Mathematical Physics, January 2021, Pleiades Publishing Ltd

    Dmitry V. Valovik

  11. On the integral characteristic function of the Sturm-Liouville problem

    Article • Sbornik Mathematics, November 2020, Institute of Physics Publishing

    Dmitry V. Valovik

  12. Об интегральной характеристической функции задачи Штурма-Лиувилля

    Article • Математический сборник, October 2020, Steklov Mathematical Institute

    Dmitry V. Valovik

  13. Operator Pencil Approach in an Electromagnetic Problem of Symmetric Wave Propagation in a Plane Shielded Waveguide

    Article • Lobachevskii Journal of Mathematics, July 2020, Pleiades Publishing Ltd

    Dmitry V. Valovik

  14. Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics

    Article • Nonlinearity, June 2020, Institute of Physics Publishing

    Dmitry V. Valovik

  15. Propagation of TM waves in a shielded dielectric waveguide filled with nonlinear anisotropic medium

    Article • May 2020, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  16. Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves

    Article • Computational Mathematics and Mathematical Physics, March 2020, Pleiades Publishing Ltd

    Dmitry V. Valovik

  17. Линеаризуемые и нелинеаризуемые решения в нелинейной задаче о собственных значениях, возникающей в теории электродинамических волноводов, заполненных нелинейной средой

    Article • Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», March 2020, Russian Institute for Scientific and Technical Information - VINITI RAS

    Dmitry V. Valovik

  18. Study of a Nonlinear Eigenvalue Problem by the Integral Characteristic Equation Method

    Article • Differential Equations, February 2020, Pleiades Publishing Ltd

    Dmitry V. Valovik

  19. Asymptotic Analysis of a Nonlinear Eigenvalue Problem Arising in the Waveguide Theory

    Article • Differential Equations, December 2019, Pleiades Publishing Ltd

    Dmitry V. Valovik

  20. Electromagnetic Symmetric Hybrid Wave Propagation Problem in a Medium with Arbitrary Nonlinear Saturation

    Article • December 2019, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  21. Многопараметрические задачи на собственные значения и их приложения в электродинамике

    Article • Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», December 2019, Russian Institute for Scientific and Technical Information - VINITI RAS

    Dmitry V. Valovik

  22. Asymptotical analysis of a nonlinear Sturm–Liouville problem: Linearisable and non-linearisable solutions

    Article • Asymptotic Analysis, September 2019, IOS Press

    Dmitry V. Valovik

  23. Perturbation of nonlinear operators in the theory of nonlinear multifrequency electromagnetic wave propagation

    Article • Communications in Nonlinear Science and Numerical Simulation, August 2019, Elsevier

    Dmitry V. Valovik

  24. Maxwell's equations with arbitrary self-action nonlinearity in a waveguiding theory: Guided modes and asymptotic of eigenvalues

    Article • Journal of Mathematical Analysis and Applications, June 2019, Elsevier

    Dmitry V. Valovik

  25. Symmetric guided electromagnetic waves in a shielded slab filled with anisotropic dielectric

    Article • June 2019, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  26. Nonlinear multiparameter eigenvalue problems: Linearised and nonlinearised solutions

    Article • Journal of Differential Equations, March 2019, Elsevier

    Dmitry V. Valovik

  27. Nonlinear multi-frequency electromagnetic wave propagation phenomena

    Article • Journal of Optics, September 2017, Institute of Physics Publishing

    Dmitry V. Valovik

  28. On the existence of infinitely many nonperturbative solutions in a transmission eigenvalue problem for nonlinear Helmholtz equation with polynomial nonlinearity

    Article • Applied Mathematical Modelling, September 2017, Elsevier

    Dmitry V. Valovik

  29. Nonlinear coupled wave propagation in a n-dimensional layer

    Article • Applied Mathematics and Computation, February 2017, Elsevier

    Dmitry V. Valovik

  30. Theory of Nonlinear Guided Electromagnetic Waves in a Plane Two-Layered Dielectric Waveguide

    Article • Mathematical Problems in Engineering, January 2017, Hindawi Publishing Corporation

    Dmitry V. Valovik

  31. О спектральных свойствах некоторых нелинейных операторов типа Штурма-Лиувилля

    Article • Математический сборник, January 2017, Steklov Mathematical Institute

    Dmitry V. Valovik

  32. Coupled electromagnetic wave propagation in a cylindrical dielectric waveguide filled with Kerr medium: nonlinear effects

    Article • Journal of Modern Optics, October 2016, Taylor & Francis

    Dmitry V. Valovik

  33. On the infinitely many nonperturbative solutions in a transmission eigenvalue problem for Maxwell’s equations with cubic nonlinearity

    Article • Journal of Mathematical Physics, October 2016, American Institute of Physics

    Dmitry V. Valovik

  34. Electromagnetic TM wave propagation in a layer with Kerr nonlinearity: Analytical results

    Article • August 2016, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  35. Ellipticity of the electric field integral equation in a problem of diffraction by a partially shielded body

    Article • August 2016, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  36. Nonlinear guided electromagnetic waves in a layer: Revisiting an old problem and new results

    Article • August 2016, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  37. Volume singular integro-differential equations in the electromagnetic diffraction problem

    Article • August 2016, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  38. Vector problem of electromagnetic wave diffraction by a system of inhomogeneous volume bodies, thin screens, and wire antennas

    Article • Journal of Electromagnetic Waves and Applications, May 2016, Taylor & Francis

    Dmitry V. Valovik

  39. On the eigenvalues of a nonlinear spectral problem

    Article • Differential Equations, February 2016, Pleiades Publishing Ltd

    Dmitry V. Valovik

  40. Nonlinear coupled electromagnetic wave propagation: Saturable nonlinearities

    Article • Wave Motion, January 2016, Elsevier

    Dmitry V. Valovik

  41. On the volume singular integro-differential equation approach for the electromagnetic diffraction problem

    Article • Applicable Analysis, November 2015, Taylor & Francis

    Dmitry V. Valovik

  42. Reply to “Comment on ‘Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity’ ”

    Article • Physical Review A, November 2015, American Physical Society (APS)

    Dmitry V. Valovik

  43. Electromagnetic TE wave propagation in a two-layered waveguide with nonlinear permittivity

    Article • May 2015, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  44. Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity

    Article • Physical Review A, January 2015, American Physical Society (APS)

    Dmitry V. Valovik

  45. Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

    Article • Advances in Mathematical Physics, January 2015, Hindawi Publishing Corporation

    Dmitry V. Valovik

  46. Integral dispersion equation method to solve a nonlinear boundary eigenvalue problem

    Article • Nonlinear Analysis Real World Applications, December 2014, Elsevier

    Dmitry V. Valovik

  47. Recent advances in the theory of coupled nonlinear guided waves

    Article • August 2014, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  48. Propagation of TE waves in a plane dielectric waveguide with nonlinear permittivity

    Article • May 2014, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  49. Coupled electromagnetic TE-TE waves propagation. Numerical approach to determine coupled propagation constants

    Article • May 2014, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  50. On the problem of propagation of nonlinear coupled TE-TM waves in a layer

    Article • Computational Mathematics and Mathematical Physics, March 2014, Pleiades Publishing Ltd

    Dmitry V. Valovik

  51. Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem

    Article • Advances in Numerical Analysis, January 2014, Hindawi Publishing Corporation

    Dmitry V. Valovik

  52. Problem of nonlinear coupled electromagnetic TE-TE wave propagation

    Article • Journal of Mathematical Physics, August 2013, American Institute of Physics

    Dmitry V. Valovik

  53. Calculation of the propagation constants of inhomogeneous nonlinear double-layer circular cylindrical waveguide by means of the Cauchy problem method

    Article • Journal of Communications Technology and Electronics, August 2013, Pleiades Publishing Ltd

    Dmitry V. Valovik

  54. Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides

    Article • Computational Mathematics and Mathematical Physics, July 2013, Pleiades Publishing Ltd

    Dmitry V. Valovik

  55. On the Problem of Electromagnetic Waves Propagating along a Nonlinear Inhomogeneous Cylindrical Waveguide

    Article • ISRN Mathematical Physics, June 2013, Hindawi Publishing Corporation

    Dmitry V. Valovik

  56. On the problem of nonlinear coupled electromagnetic transverse-electric–transverse magnetic wave propagation

    Article • Journal of Mathematical Physics, April 2013, American Institute of Physics

    Dmitry V. Valovik

  57. Coupled electromagnetic transverse-electric–transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity

    Article • Journal of Mathematical Physics, April 2013, American Institute of Physics

    Dmitry V. Valovik

  58. Electromagnetic Wave Propagation in Nonlinear Layered Waveguide Structures: Computational Approach to Determine Propagation Constants

    Article • January 2013, Springer Science + Business Media

    Dmitry V. Valovik

  59. The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for tm waves propagating in a layer with arbitrary nonlinearity

    Article • Computational Mathematics and Mathematical Physics, January 2013, Pleiades Publishing Ltd

    Dmitry V. Valovik

  60. Solution of the nonlinear eigenvalue boundary-value problem for tm electromagnetic waves propagating in a Kerr-nonlinear layer by means of the cauchy problem method

    Article • Journal of Communications Technology and Electronics, January 2013, Pleiades Publishing Ltd

    Dmitry V. Valovik

  61. Coupled electromagnetic TE-TM wave propagation in a layer with Kerr nonlinearity

    Article • Journal of Mathematical Physics, December 2012, American Institute of Physics

    Dmitry V. Valovik

  62. Electromagnetic TM wave propagation in nonlinear multilayered waveguides. Numerical technique to obtain propagation constants

    Article • August 2012, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  63. Numerical solution of the problem of propagation of TM-polarized electromagnetic waves in a nonlinear two-layered dielectric cylindrical waveguide

    Article • August 2012, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  64. Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body

    Article • Differential Equations, April 2012, Pleiades Publishing Ltd

    Dmitry V. Valovik

  65. Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity

    Article • Advances in Mathematical Physics, January 2012, Hindawi Publishing Corporation

    Dmitry V. Valovik

  66. Propagation of electromagnetic TE waves in a nonlinear medium with saturation

    Article • Journal of Communications Technology and Electronics, November 2011, Pleiades Publishing Ltd

    Dmitry V. Valovik

  67. Propagation of TM waves in a layer with arbitrary nonlinearity

    Article • Computational Mathematics and Mathematical Physics, September 2011, Pleiades Publishing Ltd

    Dmitry V. Valovik

  68. Propagation of electromagnetic waves in a nonlinear metamaterial layer

    Article • Journal of Communications Technology and Electronics, May 2011, Pleiades Publishing Ltd

    Dmitry V. Valovik

  69. Nonlinear effects in the problem of propagation of TM electromagnetic waves in a Kerr nonlinear layer

    Article • Journal of Communications Technology and Electronics, March 2011, Pleiades Publishing Ltd

    Dmitry V. Valovik

  70. Propagation of TM wave in a layer with Kerr law nonlinearity

    Article • September 2010, Institute of Electrical & Electronics Engineers (IEEE)

    Dmitry V. Valovik

  71. Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

    Article • Applied Mathematics, January 2010, Scientific Research Publishing, Inc,

    Dmitry V. Valovik

  72. Calculation of the propagation constants and fields of polarized electromagnetic TM waves in a nonlinear anisotropic layer

    Article • Journal of Communications Technology and Electronics, April 2009, Pleiades Publishing Ltd

    Dmitry V. Valovik

  73. Propagation of TM waves in a Kerr nonlinear layer

    Article • Computational Mathematics and Mathematical Physics, December 2008, Pleiades Publishing Ltd

    Dmitry V. Valovik

  74. A nonlinear boundary eigenvalue problem for TM-polarized electromagnetic waves in a nonlinear layer

    Article • Russian Mathematics, October 2008, Allerton Press

    Dmitry V. Valovik

  75. Calculation of the propagation constants of TM electromagnetic waves in a nonlinear layer

    Article • Journal of Communications Technology and Electronics, August 2008, Pleiades Publishing Ltd

    Dmitry V. Valovik