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Using “quasiphotons” to compute wave fields in an elastic medium. (English. Russian original) Zbl 0658.73015

J. Sov. Math. 38, 1620-1632 (1987); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 148, 89-103 (1985).
“Quasiphoton” solutions are constructed for longitudinal and transversal waves in an elastic medium. The “quasiphotons” are then applied to determine the fields of nonstationary high-frequency point sources in a medium with parameters dependent on two Euclidean coordinates.

MSC:

74J10 Bulk waves in solid mechanics
35L05 Wave equation
35C20 Asymptotic expansions of solutions to PDEs
74J99 Waves in solid mechanics
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References:

[1] M. M. Popov, ?A new method of wave field calculation in the high-frequency approximation,? J. Sov. Math.,20, No. 1 (1982).
[2] V. E. Grikurov and M. M. Popov, ?Summation of Gaussian beams in a surface waveguide,? Wave Motion, No. 5, 225?233 (1983). · Zbl 0511.73020 · doi:10.1016/0165-2125(83)90013-6
[3] A. P. Kachalov and M. M. Popov, ?Application of Gaussian beams in isotropic elasticity theory,? Preprint LOMI R-9-82 [in Russian], LOMI AN SSSR (1982), pp. 3?14.
[4] V. M. Babich and V. V. Ulin, ?A complex space-time ray method and ?quasiphotons?,? J. Sov Math.,24, No. 3 (1984). · Zbl 0532.35007
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[7] G. I. Petrashen’, ?Fundamentals of the mathematical theory of elastic wave propagation,? Topics in the Dynamic Theory of Seismic Wave Propagation [in Russian], No. 18, Leningrad (1978), pp. 3?247.
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