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Trofimov Vyacheslav Anatol'evich

Publications in Math-Net.Ru

  1. Heating of a metal layer by a scanning laser beam

    Optics and Spectroscopy, 131:3 (2023),  396–406
  2. Highly efficient third harmonic generation in quadratic and cubic nonlinear media by cascaded second harmonic generation

    Kvantovaya Elektronika, 53:8 (2023),  645–660
  3. Refraction by gas inhomogeneities during laser heating of a metal

    Optics and Spectroscopy, 130:4 (2022),  595–596
  4. Simulation of broadening the second harmonic spectrum in KDP by chirp pulse pumping

    J. Sib. Fed. Univ. Math. Phys., 14:2 (2021),  144–149
  5. Propagation of a self-similar pulse in a medium with one-photon transient absorption

    Optics and Spectroscopy, 124:4 (2018),  499–503
  6. Femtosecond pulse self-shortening in Kerr media: role of modulational instability in the spectrum formation

    Kvantovaya Elektronika, 48:4 (2018),  306–312
  7. Self-phase modulation in a thin fused silica plate upon interaction with a converging beam of down-chirped femtosecond radiation

    Kvantovaya Elektronika, 45:5 (2015),  415–420
  8. Spectral broadening and self-compression of negatively chirped visible femtosecond pulses in fused silica

    Kvantovaya Elektronika, 42:12 (2012),  1097–1099
  9. Numerical method for finding 3D solitons of the nonlinear Schrödinger equation in the axially symmetric case

    Zh. Vychisl. Mat. Mat. Fiz., 49:11 (2009),  1988–2000
  10. Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 48:4 (2008),  713–724
  11. Conservative finite-difference scheme for the problem of a femtosecond laser pulse with an axially symmetric profile propagating in a medium with cubic nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007),  1752–1773
  12. On the efficiency of some difference schemes for problems of nonlinear interaction of optical radiation with a semiconductor

    Differ. Uravn., 42:8 (2006),  1123–1131
  13. Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006),  2254–2264
  14. Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a nonlinear photonic crystal with nonreflecting boundary conditions

    Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006),  161–171
  15. Conservative Difference Schemes for Some Problems of Femtosecond Nonlinear Optics

    Differ. Uravn., 41:7 (2005),  908–917
  16. Difference scheme for the problem of femtosecond pulse interaction with a semiconductor in the case of nonlinear mobility

    Zh. Vychisl. Mat. Mat. Fiz., 45:12 (2005),  2185–2196
  17. The conservative difference scheme for the problem of femtosecond laser pulse propagation through a medium with a cubic nonlinearity

    Zh. Vychisl. Mat. Mat. Fiz., 43:11 (2003),  1709–1721
  18. A conservative difference scheme for the problem of two-wave interaction of femtosecond pulses in photonic crystals

    Zh. Vychisl. Mat. Mat. Fiz., 43:10 (2003),  1530–1535
  19. Invariants of nonlinear propagation of femtosecond laser pulses through a medium with non-stationary response

    Zh. Vychisl. Mat. Mat. Fiz., 42:12 (2002),  1831–1835
  20. Invariants of nonlinear interaction of femtosecond pulses in the presence of third-order dispersion

    Zh. Vychisl. Mat. Mat. Fiz., 42:5 (2002),  709–717
  21. Invariants of femtosecond pulse propagation in photonic crystals

    Zh. Vychisl. Mat. Mat. Fiz., 41:9 (2001),  1429–1433
  22. Bistability and uniqueness of solutions in the problem of second harmonic generation of femtosecond pulses

    Zh. Vychisl. Mat. Mat. Fiz., 41:8 (2001),  1275–1288
  23. Optical bistability based on nonlinear oblique reflection of light beams from a screen with an aperture on its axis

    Kvantovaya Elektronika, 26:2 (1999),  147–150
  24. Invariants of multiwave nonlinear interaction of femtosecond laser pulses

    Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999),  1740–1748
  25. An invariant of femtosecond-pulse propagation in a nonlinear absorptive medium

    Zh. Vychisl. Mat. Mat. Fiz., 38:12 (1998),  2055–2059
  26. On a new approach to the simulation of the nonlinear propagation of ultrashort laser pulses

    Zh. Vychisl. Mat. Mat. Fiz., 38:5 (1998),  835–839
  27. Optical bistability in semiconductors under the condition of finite time of absorpted light energy thermalization. II. Numerical simulation of spatial switching waves

    Mat. Model., 5:4 (1993),  14–31
  28. Optical bistability in semiconductors under the condition of finite time of absorpted light energy thermalization. I. Numerical methods. Bistability conditions

    Mat. Model., 5:4 (1993),  3–13
  29. Mathematical modeling of an optical absorption bistability based on a semiconductor system under the condition of two-dimensional thermal conductivity

    Mat. Model., 4:7 (1992),  31–48
  30. The mathematical modeling of the thermal self-action of the scaned light waves

    Mat. Model., 4:3 (1992),  84–90
  31. Minimization of the angular divergence of optical radiation transmitted by a nonlinear layer

    Kvantovaya Elektronika, 19:3 (1992),  241–245
  32. Difference schemes for problems of absorption bistability in semiconductors

    Differ. Uravn., 27:7 (1991),  1185–1196
  33. Numerical methods for problems of the stimulation of chemical reactions in gases by optical radiation under conditions of developed thermodiffusion

    Differ. Uravn., 27:7 (1991),  1177–1185
  34. On numerical algorithm for nonlinear differential equations describing some processes in photoreciever

    Mat. Model., 3:10 (1991),  95–103
  35. Mathematical simulation of nonstationary interaction of two light waves in a resonantly absorbing gas

    Mat. Model., 3:2 (1991),  20–29
  36. Four-wave lasing in a resonantly absorbing gas with amplification in a feedback loop

    Kvantovaya Elektronika, 18:8 (1991),  972–977
  37. Dynamics of four-wave oscillation due to a thermal nonlinearity with amplification in a feedback loop

    Kvantovaya Elektronika, 18:6 (1991),  732–737
  38. Mathematical simulation of the optical âistability on the thermal nonlinearity of a semiconductor

    Mat. Model., 2:12 (1990),  17–32
  39. About modeling of macrokinetic of gas reactions under influence of optical radiation

    Mat. Model., 2:10 (1990),  80–90
  40. Interaction of optical waves in absorbing media with thermal nonlinearity mechanism

    Mat. Model., 2:10 (1990),  26–37
  41. Numerical methods for problems of stimulating chemical reactions in a gas by a light pulse

    Differ. Uravn., 25:7 (1989),  1219–1227
  42. Numerical methods for problems describing heat self-interaction of optical radiation

    Mat. Model., 1:10 (1989),  130–141
  43. Homologies of complete Brouwer lattices

    Uspekhi Mat. Nauk, 44:3(267) (1989),  159–160
  44. A difference method for solving a problem on the steady-state propagation of a light beam in a chemically active gas medium

    Differ. Uravn., 24:7 (1988),  1192–1196
  45. Adaptive focusing of an optical beam by a system with delay in the control channel

    Kvantovaya Elektronika, 15:11 (1988),  2379–2381
  46. Reduction of the response time of adaptive control of the wavefront of a light beam

    Kvantovaya Elektronika, 14:11 (1987),  2261–2263
  47. Nonlinear distortions of elliptical light beams

    Kvantovaya Elektronika, 14:9 (1987),  1839–1848
  48. Reflexive and self-dual Hilbert modules over certain $C^*$-algebras

    Uspekhi Mat. Nauk, 42:2(254) (1987),  247–248
  49. Compensation of nonlinear distortions of light beams in the case of restricted deformation of the control mirror

    Kvantovaya Elektronika, 13:7 (1986),  1484–1495
  50. Difference methods in problems of the propagation of optical radiation in a cloud medium

    Differ. Uravn., 21:7 (1985),  1186–1191
  51. Compensation of nonlinear distortions of scanning light beams

    Kvantovaya Elektronika, 12:8 (1985),  1617–1627
  52. Compensation of nonlinear distortions of light pulses by an adaptive flexible mirror under different control geometry conditions

    Kvantovaya Elektronika, 12:2 (1985),  355–360
  53. Compensation of nonlinear distortions of optical radiation

    Kvantovaya Elektronika, 11:4 (1984),  693–700
  54. A sum of internal relations as a classification performance index

    Avtomat. i Telemekh., 1976, no. 3,  133–141
  55. Algorithm for the analysis of the structure of connection matrices

    Avtomat. i Telemekh., 1975, no. 11,  170–180

© Steklov Math. Inst. of RAS, 2026