Mathematical problems in the theory of wave propagation.
Main publications:
A. B. Plachenov, “Nestatsionarnye normalnye volny tonkogo izognutogo volnovoda v mnogoluchevoi oblasti (ravnomernaya asimptotika)”, Interferentsionnye volny v sloistykh sredakh. I, Zap. nauchn. sem. LOMI, 99, Izd-vo «Nauka», Leningrad. otd., L., 1980, 127–137
V. N. Kudashov, A. B. Plachenoe, A. M. Radin, “Fundamentalnaya poperechnaya moda trekhmernogo koltsevogo rezonatora, soderzhaschego selektiruyuschie elementy”, Optika i spektroskopiya, 93:5 (2002), 843–852
V. N. Kudashov, A. B. Plachenov, A. M. Radin, “Mody trekhmernykh opticheskikh rezonatorov, soderzhaschikh selektiruyuschie elementy”, Zhurnal tekhnicheskoi fiziki, 73:11 (2003), 111–117
A. B. Plachenov, A. M. Radin, V. N. Kudashov, “Poluchenie yavnykh formul dlya fundamentalnoi mody rezonatora v vide gaussovskogo puchka so slozhnym astigmatizmom”, Radiotekhnika i elektronika, 52:12 (2007), 1422–1429
A. B. Plachenov, V. N. Kudashov, A. M. Radin, “Analiticheskoe opisanie gaussova puchka v koltsevom rezonatore s nekomplanarnym osevym konturom i chetnym chislom zerkal”, Kvantovaya elektronika, 39:3 (2009), 261–272
I. A. So, A. B. Plachenov, A. P. Kiselev, “Unidirectional single-cycle and sub-cycle pulses”, Optics and Spectroscopy, 128:12 (2020), 1865–1867; Optics and Spectroscopy, 128:12 (2020), 2000–2001
A. B. Plachenov, “Acoustic, electromagnetic and elastic wavefield energy expression via its asymptotics at large times and distances”, Zap. Nauchn. Sem. POMI, 493 (2020), 269–287
A. B. Plachenov, “Bessel–Gaussian shifted paraxial beams: I”, Optics and Spectroscopy, 126:3 (2019), 311–318; Optics and Spectroscopy, 126:3 (2019), 232–239
A. B. Plachenov, B. T. Plachenov, “Border effect, fractal structures and brightness oscillations in non-silver photographic materials”, Nanosystems: Physics, Chemistry, Mathematics, 6:1 (2015), 133–139
2011
5.
A. B. Plachenov, A. M. Radin, “Analytical description of a Gaussian beam in a ring resonator with a nonplanar axial contour and an odd number of mirrors”, Kvantovaya Elektronika, 41:1 (2011), 43–54 [Quantum Electron., 41:1 (2011), 43–54]
6.
A. B. Plachenov, “Tilted nonparaxial beams and packets for the wave equation with two spatial variables”, Zap. Nauchn. Sem. POMI, 393 (2011), 224–233; J. Math. Sci. (N. Y.), 185:4 (2012), 638–643
A. P. Kiselev, A. B. Plachenov, “Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution”, Zap. Nauchn. Sem. POMI, 393 (2011), 167–177; J. Math. Sci. (N. Y.), 185:4 (2012), 605–610
A. B. Plachenov, V. N. Kudashov, A. M. Radin, “Analytical description of a Gaussian beam in a ring resonator with a nonplanar axial contour and an even number of mirrors”, Kvantovaya Elektronika, 39:3 (2009), 261–272 [Quantum Electron., 39:3 (2009), 261–272]
A. B. Plachenov, V. N. Kudashov, A. M. Radin, “Analytic method for the construction of the fundamental mode of a resonator in the form of a Gaussian beam with complex astigmatism”, Kvantovaya Elektronika, 37:3 (2007), 290–298 [Quantum Electron., 37:3 (2007), 290–298]
V. N. Kudashov, A. B. Plachenov, A. M. Radin, “Complex <i>ABCD</i> transformations for optical ring cavities with losses and gain”, Kvantovaya Elektronika, 27:1 (1999), 87–92 [Quantum Electron., 29:4 (1999), 368–373]
A. B. Plachenov, “Nonstationary modes of a thin and curved waveguide in a multiray zone (the uniform asymptotics)”, Zap. Nauchn. Sem. LOMI, 99 (1980), 127–137; J. Soviet Math., 20:5 (1982), 2478–2486
1979
12.
I. A. Molotkov, A. B. Plachenov, “Ungtationary modes in a thin and curved waveguide of variable width”, Zap. Nauchn. Sem. LOMI, 89 (1979), 210–218; J. Soviet Math., 19:4 (1982), 1447–1453
Contact us: