Kachalov, A. P. 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. Cited in 2 Documents MSC: 74J10 Bulk waves in solid mechanics 35L05 Wave equation 35C20 Asymptotic expansions of solutions to PDEs 74J99 Waves in solid mechanics Keywords:Gaussian beam summation method; space-time Gaussian beams; eikonal equation; transport equation; three-dimensional inhomogeneous medium; center of expansion; center of rotation; longitudinal; transversal waves; fields of nonstationary high-frequency point sources PDFBibTeX XMLCite \textit{A. P. Kachalov}, J. Sov. Math. 38, 1620--1632 (1987; Zbl 0658.73015); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 148, 89--103 (1985) Full Text: DOI 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 [5] A. P. Kachalov, ?A coordinate system for the description of a ?quasiphoton?,? J. Sov. Math.,32, No. 2 (1986). · Zbl 0584.35088 [6] V. M. Babich, V. S. Buldyrev, and I. A. Moltkov, The Space-Time Ray Method. Linear and Nonlinear Waves [in Russian], Leningrad (1985). [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.