Tilted nonparaxial beams and packets for the wave equation with two spatial variables
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 224-233 Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of relatively nondistorted solutions of the wave equation in two-dimension space is constructed. This class includes nonharmonic in time tilted beam-like and packetlike solutions with Gaussian-type localization.
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A. B. Plachenov. Tilted nonparaxial beams and packets for the wave equation with two spatial variables. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 224-233. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a15/

[1] R. Kurant, D. Gilbert, Metody matematicheskoi fiziki, Gostekhizdat, M., 1941

[2] G. Beitmen, Matematicheskaya teoriya rasprostraneniya elektromagnitnykh voln, Nauka, M., 1958

[3] P. Hillion, “Generalized phases and nondispersive waves”, Acta Appl. Math., 30:1 (1993), 35–45 | DOI | MR | Zbl

[4] A. P. Kiselev, M. V. Perel, “Otnositelno neiskazhayuschiesya resheniya $m$-mernogo volnovogo uravneniya”, Diff. uravneniya, 38:8 (2002), 1128–1129 | MR | Zbl

[5] A. P. Kiselev, “Lokalizovannye svetovye volny: paraksialnye i tochnye resheniya volnovogo uravnenya (Obzor)”, Optika i Spektroskopiya, 102:4 (2007), 661–681 | MR

[6] A. Torre, “Relativistic Laguerre polynomials and splash pulses”, Progress in Electromagnetics Research B, 13 (2009), 329–356 | DOI

[7] A. P. Kiselev, A. B. Plachenov, “Tochnye resheniya $m$-mernogo volnovogo uravneniya iz paraksialnykh. Dalneishee obobschenie resheniya Beitmena”, Zap. nauchn. semin. POMI, 393, 2011, 167–177 | MR

[8] A. P. Kiselev, M. V. Perel, “Highly localized solutions of the wave equation”, J. Math. Phys., 41:4 (2000), 1934–1955 | DOI | MR | Zbl

[9] J. N. Brittingham, “Focus waves modes in homogeneous Maxwell's equations: Transverse electric mode”, J. Appl. Phys., 54 (1983), 1179–1189 | DOI

[10] A. P. Kiselev, “Modulirovannye gaussovy puchki”, Izv. vyssh. uch. zaved. Radiofizika, 26:5 (1983), 1014–1020 | MR

[11] I. M. Besieris, A. M. Shaarawi, R. W. Ziolkowski, “A bidirectional traveling plane wave representation of exact solutions of the wave equation”, J. Math. Phys., 30 (1989), 1254–1269 | DOI | MR | Zbl

[12] R. W. Ziolkowski, “Localized transmission of electromagnetic energy”, Phys. Rev. A, 39 (1989), 2005–2033 | DOI | MR

[13] M. M. Popov, “Sobstvennye kolebaniya mnogozerkalnykh rezonatorov”, Vestn. Leningr. un-ta, ser. fiz.-khim., 1969, no. 22(4), 42–54 | MR

[14] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, GRFML, M., 1977 | MR

[15] Yu. A. Ananev, Opticheskie rezonatory i lazernye puchki, Nauka, GRFML, M., 1980 | Zbl

[16] Y. Hadad, T. Melamed, “Parametrization of the tilted Gaussian beam waveobjects”, Progress in Electromagnetics Research, 102 (2010), 65–80 | DOI