Popov, M. M. A new method of computing wave fields in the high-frequency approximation. (English. Russian original) Zbl 0489.73039 J. Sov. Math. 20, 1869-1882 (1982); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 104, 195-216 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 Documents MSC: 74J99 Waves in solid mechanics 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35B40 Asymptotic behavior of solutions to PDEs Keywords:wave fields; high-frequency approximation; summation of Gaussian pencils at point of observation; each pencil connected with ray passing in neighborhood of point; integral over Gaussian pencils × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. M. Babich, ?The ray method of computing the intensity of wave fronts,? Dokl. Akad. Nauk SSSR,110, No. 3, 355?357 (1956). [2] V.M. Babich and A. S. Alekseev, ?On the ray method of computing the intensity of wave fronts,? Izv. Akad. Nauk SSSR, Ser. Geofiz., No. 1, 17?31 (1958). [3] V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972). · Zbl 0255.35002 [4] V. ?erveny, I. A. Molotkov, and I. P?en?ik, The Ray Method in Seismology, Praha, Univerzita Karlova (1977). [5] V. P. Maslov, Perturbation Theory and Asymptotics Methods [in Russian], Moscow (1965). [6] V. M. Babich and T. F. Pankratova, ?On discontinuities of the Green function of the mixed problem for the wave equation with a variable coefficient,? in: Probl. Mat. Fiz., Leningrad (1973), pp. 9?27. [7] T. F. Pankratova, ?On the proper oscillations in an annular resonator,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,15, 122?141 (1969). [8] N. Ya. Kirpichnikova, ?On the construction of solutions of the equations of the theory of elasticity which are concentrated near rays for an inhomogeneous, isotropic space,? Tr. Mosk. Inst. Akad. Nauk,115, 103?133 (1971). [9] M. M. Popov, ?On a method of computing the geometric divergence in an inhomogeneous medium containing a boundary of separation,? Dokl. Akad. Nauk SSSR,237, No. 5, 1059?1062 (1977). [10] M. M. Popov and I. Psencik, ?Ray amplitudes in inhomogeneous media with curved interfaces,? Geofysikalni Sb. XXIV (1976), Praha (1978), pp. 111?129. [11] M. M. Popov, I. P?en?ik, and V. ?erveny, ?Uniform ray asymptotics for seismic wave fields in laterally inhomogeneous media,? EGS Meeting, Budapest (1980). [12] M. M. Popov and I. Psencik, ?Computation of ray amplitudes in inhomogeneous media with curved interfaces,? Stud. Geoph. Geod.,22, 248?258 (1978). · doi:10.1007/BF01627902 [13] M. V. Fedoryuk, The Method of Descent [in Russian], Moscow (1977). · Zbl 0463.41020 [14] M. M. Popov and L. G. Tyurikov, ?On two approaches to the computation of the geometric divergence in an inhomogeneous, isotropic medium,? in: Vopr. Dinam. Teor. Raspr. Seism. Voln, Vol. 20 (1980), pp. 61?68. [15] V. I. Smirnov, A Course of Higher Mathematics, Vol. 3, Part 1, Pergamon (1964). · Zbl 0121.25904 [16] V. M. Babich and N. Ya. Kirpichnikova, The Method of the Boundary Layer in Diffraction Problems [in Russian], Leningrad (1974). · Zbl 0411.35001 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.