The space-time ray method and quasiphotons. (English. Russian original) Zbl 1176.81170

J. Math. Sci., New York 148, No. 5, 633-638 (2008); translation from Zap. Nauchn. Semin. POMI 342, 5-13 (2007).
Summary: A new approach to the construction of qusiphotons is illustrated with the example of quasiphotons of the wave equation with a variable velocity.


81V80 Quantum optics
35L05 Wave equation
Full Text: DOI


[1] V. M. Babich and Yu. P. Danilov, ”Construction of the asymptotics of the solution of the Schrö dinger equation, which is concentrated in a neighborhood of the classical trajectory,” Zap. Nauchn. Semin. LOMI, 15, 47–65 (1969).
[2] V. M. Maslov, The Complex WKB Method in Nonlinear Equations [in Russian], Nauka, Moscow (1977). · Zbl 0449.58001
[3] V. N. Babich and V. V. Ulin, ”The complex ST ray method and quasiphotons,” Zap. Nauchn. Semin. LOMI, 117, 5–11 (1981). · Zbl 0477.35025
[4] J. Ralston, ”Gaussian beams and the propagation of singularities,” MAA Studies Math., 21, 206–248 (1982). · Zbl 0533.35062
[5] A. P. Kachalov, ”A system of coordinates in the description of quasiphotons,” Zap. Nauchn. Semin. LOMI, 140, 73–76 (1984). · Zbl 0557.35096
[6] V. M. Babich, V. S. Buldyrev, and L. A. Molotkov, Space-Time Ray Method [in Russian], Leningrad (1985). · Zbl 0678.35002
[7] V. G. Bagrov, V. V. Belov, and A. Yu. Trifonov, ”Semiclassical trajectory-coherent approximation in quantum mechanics,” Ann. Phys., 246, No. 2, 231–290 (1996). · Zbl 0874.35099
[8] A. P. Kachalov, ”Nonstationary electromagnetic Gaussian beams in inhomogeneous anisotropic media,” Zap. Nauchn. Semin. POMI, 264, 83–100 (2000). · Zbl 1003.78001
[9] V. V. Belov, A. Yu. Trifonov, and A. V. Shapovalov, ”Semiclassical trajectory-coherent approximation for equations of the Hartri type,” Teor. Mat. Fiz., 130, No. 2, 460–492 (2002).
[10] S. Bochner and U. T. Martin, Functions of Many Complex Variables [Russian translation], Moscow (1951).
[11] V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 4, P. 2, Nauka, Moscow (1981). · Zbl 0742.00001
[12] R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964). · Zbl 0121.07801
[13] V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of Diffraction of Short Waves [in Russian], Nauka, Moscow (1972). · Zbl 0255.35002
[14] G. Witham, Linear and Nonlinear Waves [Russian translation], Nauka, Moscow (1977).
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