Nonlinear eigenvalue problems for Maxwells equations.
Main publications:
Valovik D.V., “On the problem of nonlinear coupled electromagnetic transverse-
electric.transverse-magnetic wave propagation”, Journal of Mathematical Physics, 54:4 (2013), 042902 (14 pages)
Valovik D.V., “Integral dispersion equation method to solve a nonlinear boundary eigenvalue problem”, Nonlinear Analysis: Real World Applications, 20 (2014), 52–58
Smirnov Yu.G., Valovik D.V., “Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity”, Physical Review A, 92:1 (2015), 013840 (6 pages)
Smirnov Yu.G., Valovik D.V., “On the infinitely many nonperturbative solutions in a
transmission eigenvalue problem for Maxwell.s equations with cubic nonlinearity”, Journal of Mathematical Physics, 57:10 (2016), 103504 (15 pages)
Valovik D.V., “Novel propagation regimes for TE waves guided by a waveguide filled with
Kerr medium”, Journal of Nonlinear Optical Physics & Materials, 25:4 (2016), 1650051 (17 pages)
D. V. Valovik, S. V. Tikhov, “Existence of solutions of a nonlinear eigenvalue problem and their properties”, Mat. Sb., 215:1 (2024), 59–81; Sb. Math., 215:1 (2024), 52–73
2.
D. V. Valovik, A. A. Dyundyaeva, S. V. Tikhov, “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; Comput. Math. Math. Phys., 64:10 (2024), 2351–2367
2021
3.
D. V. Valovik, “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; Comput. Math. Math. Phys., 61:1 (2021), 103–117
D. V. Valovik, S. V. Tikhov, “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.
D. V. Valovik, “On the integral characteristic function of the Sturm-Liouville problem”, Mat. Sb., 211:11 (2020), 41–53; Sb. Math., 211:11 (2020), 1539–1550
D. V. Valovik, “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; Comput. Math. Math. Phys., 60:3 (2020), 427–447
D. V. Valovik, V. Yu. Kurseeva, “Multiparameter eigenvalue problems and their applications in electrodynamics”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 172 (2019), 9–29
8.
D. V. Valovik, “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; Comput. Math. Math. Phys., 59:6 (2019), 958–977
D. V. Valovik, S. V. Tikhov, “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; Comput. Math. Math. Phys., 58:10 (2018), 1600–1609
E. O. Biteleva, D. V. Valovik, “A note on hybrid waves in plane layered waveguiding structures”, University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 3, 3–14
11.
D. V. Valovik, “The spectral properties of some nonlinear operators of Sturm-Liouville type”, Mat. Sb., 208:9 (2017), 26–41; Sb. Math., 208:9 (2017), 1282–1297
D. V. Valovik, A. E. Demchenko, “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
2015
14.
D. V. Valovik, M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “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
D. V. Valovik, Yu. G. Smirnov, “On the problem of propagation of nonlinear coupled TE–TM waves in a layer”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 504–518; Comput. Math. Math. Phys., 54:3 (2014), 522–536
D. V. Valovik, E. A. Marennikova, Yu. G. Smirnov, “A nonlinear transmission eigenvalue problem that describes electromagnetic ТЕ wave propagation in a plane inhomogeneous nonlinear dielectric waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 2, 50–63
17.
D. V. Valovik, Yu. G. Smirnov, E. Yu. Smol'kin, “Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1150–1161; Comput. Math. Math. Phys., 53:7 (2013), 973–983
D. V. Valovik, E. V. Zarembo, “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; Comput. Math. Math. Phys., 53:1 (2013), 78–92
D. V. Valovik, E. R. Ergasheva, “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.
D. V. Valovik, Yu. G. Smirnov, “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.
D. V. Valovik, E. Yu. Smol'kin, “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
Yu. G. Smirnov, S. N. Kupriyanova, D. V. Valovik, “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.
D. V. Valovik, “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.
D. V. Valovik, Yu. G. Smirnov, E. A. Shirokova, “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
D. V. Valovik, “Propagation of TM waves in a layer with arbitrary nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 51:9 (2011), 1729–1739; Comput. Math. Math. Phys., 51:9 (2011), 1622–1632
D. V. Valovik, Yu. G. Smirnov, “Collocation method for solving the electric field equation”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 4, 89–100
27.
D. V. Valovik, Yu. G. Smirnov, “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.
D. V. Valovik, “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
D. V. Valovik, Yu. G. Smirnov, “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
D. V. Valovik, “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
D. V. Valovik, Yu. G. Smirnov, “A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10, 70–74; Russian Math. (Iz. VUZ), 52:10 (2008), 60–63
D. V. Valovik, Yu. G. Smirnov, “Propagation of TM waves in a Kerr nonlinear layer”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2186–2194; Comput. Math. Math. Phys., 48:12 (2008), 2217–2225
D. V. Valovik, Yu. G. Smirnov, “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
Yu. G. Smirnov, D. V. Valovik, “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
2008
35.
D. V. Valovik, “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
Contact us: