Babich, V. M. A point source of electromagnetic waves in an inhomogeneous medium: a high frequency ansatz and the dual nonstationary singular solution. (English. Russian original) Zbl 1435.35370 J. Math. Sci., New York 243, No. 5, 634-639 (2019); translation from Zap. Nauchn. Semin. POMI 471, 7-14 (2018). MSC: 35Q61 78A25 78A40 35B40 42A38 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 243, No. 5, 634--639 (2019; Zbl 1435.35370); translation from Zap. Nauchn. Semin. POMI 471, 7--14 (2018) Full Text: DOI OpenURL
Babich, V. M. Solution of the diffraction problem of a plane wave by an impedance wedge (non-stationary case. Smirnov-Sobolev method). (English) Zbl 1321.35123 Russ. J. Math. Phys. 22, No. 2, 145-152 (2015). MSC: 35Q15 78A46 PDF BibTeX XML Cite \textit{V. M. Babich}, Russ. J. Math. Phys. 22, No. 2, 145--152 (2015; Zbl 1321.35123) Full Text: DOI OpenURL
Babich, V. M. Formal power series and their applications in the mathematical theory of diffraction. (English. Russian original) Zbl 1303.78003 J. Math. Sci., New York 194, No. 1, 1-7 (2013); translation from Zap. Nauchn. Sem. POMI 409, 5-16 (2012). MSC: 78A45 35C20 78M35 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 194, No. 1, 1--7 (2013; Zbl 1303.78003); translation from Zap. Nauchn. Sem. POMI 409, 5--16 (2012) Full Text: DOI OpenURL
Babich, V. M. A class of topographical waveguides. (English. Russian original) Zbl 1210.35261 St. Petersbg. Math. J. 22, No. 1, 73-79 (2011); translation from Algebra Anal. 22, No. 1, 98-107 (2010). MSC: 35Q86 74L05 35P05 86A15 78A50 PDF BibTeX XML Cite \textit{V. M. Babich}, St. Petersbg. Math. J. 22, No. 1, 73--79 (2011; Zbl 1210.35261); translation from Algebra Anal. 22, No. 1, 98--107 (2010) Full Text: DOI OpenURL
Kamotskii, V. V.; Fradkin, L. Ju.; Samokish, B. A.; Borovikov, V. A.; Babich, V. M. On Budaev and Bogy’s approach to diffraction by the 2D traction-free elastic wedge. (English) Zbl 1223.74022 SIAM J. Appl. Math. 67, No. 1, 235-259 (2006). MSC: 74J25 35J05 47B35 78A45 PDF BibTeX XML Cite \textit{V. V. Kamotskii} et al., SIAM J. Appl. Math. 67, No. 1, 235--259 (2006; Zbl 1223.74022) Full Text: DOI arXiv OpenURL
Babich, V. M.; Kuznetsov, A. V. On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions. (Russian, English) Zbl 1092.35108 Zap. Nauchn. Semin. POMI 324, 5-19 (2005); translation in J. Math. Sci., New York 138, No. 2, 5483-5490 (2006). Reviewer: Johannes Elschner (Berlin) MSC: 35Q60 78A40 78M35 PDF BibTeX XML Cite \textit{V. M. Babich} and \textit{A. V. Kuznetsov}, Zap. Nauchn. Semin. POMI 324, 5--19 (2005; Zbl 1092.35108); translation in J. Math. Sci., New York 138, No. 2, 5483--5490 (2006) Full Text: EuDML Link OpenURL
Babich, V. M. Propagation of creeping waves along the curvilinear surface of an anisotropic elastic body. (English. Russian original) Zbl 1116.74029 J. Math. Sci., New York 127, No. 6, 2340-2352 (2005); translation from Zap. Nauchn. Semin. POMI 297, 9-29 (2003). MSC: 74J15 35J25 78A05 78A45 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 127, No. 6, 2340--2352 (2003; Zbl 1116.74029); translation from Zap. Nauchn. Semin. POMI 297, 9--29 (2003) Full Text: DOI OpenURL
Smyshlyaev, V. P.; Babich, V. M.; Dementiev, D. B.; Samokish, B. A. Diffraction of creeping waves by conical points. (English) Zbl 1077.78505 Abrahams, I. David (ed.) et al., IUTAM symposium on diffraction and scattering in fluid mechanics and elasticity. Proceedings of the IUTAM symposium, Manchester, United Kingdom, July 16–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0590-3/hbk). Fluid Mech. Appl. 68, 179-187 (2002). MSC: 78A45 78M25 PDF BibTeX XML Cite \textit{V. P. Smyshlyaev} et al., Fluid Mech. Appl. 68, 179--187 (2002; Zbl 1077.78505) Full Text: DOI OpenURL
Babich, V. M.; Dement’ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P. Scattering of high-frequency electromagnetic waves by the vertex of a perfectly conducting cone (singular directions). (English. Russian original) Zbl 1108.78007 J. Math. Sci., New York 122, No. 5, 3453-3458 (2004); translation from Zap. Nauchn. Semin. POMI 285, 5-14 (2002). MSC: 78A45 PDF BibTeX XML Cite \textit{V. M. Babich} et al., J. Math. Sci., New York 122, No. 5, 3453--3458 (2002; Zbl 1108.78007); translation from Zap. Nauchn. Semin. POMI 285, 5--14 (2002) Full Text: DOI OpenURL
Babich, V. M. On the reciprocity principle in the scattering of plane electromagnetic waves by a conic scatterer. (English. Russian original) Zbl 1108.78006 J. Math. Sci., New York 117, No. 2, 3895-3899 (2003); translation from Zap. Nauchn. Semin. POMI 275, 17-24 (2001). MSC: 78A45 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 117, No. 2, 3895--3899 (2001; Zbl 1108.78006); translation from Zap. Nauchn. Semin. POMI 275, 17--24 (2001) Full Text: DOI OpenURL
Babich, V. M.; Kamotskii, V. V. The wave field near the point of incidence of the limiting ray. (English. Russian original) Zbl 1106.78303 J. Math. Sci., New York 111, No. 4, 3632-3638 (2002); translation from Zap. Nauchn. Semin. POMI 264, 22-32 (2000). MSC: 78A45 35A18 35Q60 PDF BibTeX XML Cite \textit{V. M. Babich} and \textit{V. V. Kamotskii}, J. Math. Sci., New York 111, No. 4, 1 (2000; Zbl 1106.78303); translation from Zap. Nauchn. Semin. POMI 264, 22--32 (2000) Full Text: DOI OpenURL
Babich, V. M.; Dement’ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P. Scattering of a high-frequency wave by the vertex of an arbitrary cone (singular directions). (English. Russian original) Zbl 1003.78006 J. Math. Sci., New York 111, No. 4, 3623-3631 (2002); translation from Zap. Nauchn. Semin. POMI 264, 7-21 (2000). MSC: 78A45 PDF BibTeX XML Cite \textit{V. M. Babich} et al., J. Math. Sci., New York 111, No. 4, 1 (2000; Zbl 1003.78006); translation from Zap. Nauchn. Semin. POMI 264, 7--21 (2000) Full Text: DOI OpenURL
Babich, Vassilii M.; Dement’ev, Daniel B.; Samokish, Boris A.; Smyshlyaev, Valery P. On evaluation of the diffraction coefficients for arbitrary ”nonsingular” directions of a smooth convex cone. (English) Zbl 0992.78016 SIAM J. Appl. Math. 60, No. 2, 536-573 (2000). Reviewer: Ll.G.Chambers (Bangor) MSC: 78A45 35J05 35Q60 78M35 PDF BibTeX XML Cite \textit{V. M. Babich} et al., SIAM J. Appl. Math. 60, No. 2, 536--573 (2000; Zbl 0992.78016) Full Text: DOI OpenURL
Babich, V. M.; Kamotskii, V. V. Computation of the scattering amplitude of a wave diffracted by the vertex of a cone of arbitrary shape. (English. Russian original) Zbl 0978.35071 J. Math. Sci., New York 108, No. 5, 635-641 (2002); translation from Zap. Nauchn. Semin. POMI. 257, 7-15 (1999). MSC: 35Q60 78A45 78M35 PDF BibTeX XML Cite \textit{V. M. Babich} and \textit{V. V. Kamotskii}, J. Math. Sci., New York 108, No. 5, 635--641 (1999; Zbl 0978.35071); translation from Zap. Nauchn. Semin. POMI. 257, 7--15 (1999) Full Text: DOI OpenURL
Babich, V. M.; Lyalinov, M. A. Scattering of waves by an expanding surface. (English. Russian original) Zbl 0982.78011 J. Math. Sci., New York 102, No. 4, 4147-4165 (2000); translation from Zap. Nauchn. Semin. POMI 250, 35-48 (1998). Reviewer: A.Jeffrey (Newcastle upon Tyne) MSC: 78A45 35Q60 35L05 PDF BibTeX XML Cite \textit{V. M. Babich} and \textit{M. A. Lyalinov}, J. Math. Sci., New York 102, No. 4, 4157--4165 (1998; Zbl 0982.78011); translation from Zap. Nauchn. Semin. POMI 250, 35--48 (1998) Full Text: DOI OpenURL
Babich, V. M.; Samokish, B. A.; Demen’tev, D. B. Diffraction of a plane wave by a narrow cone. (Russian. English summary) Zbl 0900.35279 Ladyzhenskaya, O. A. (ed.), Boundary value problems of mathematical physics and adjacent problems of function theory. 26. Work collection. Dedicated to N. N. Ural’tseva on her anniversary. Sankt-Peterburg: Nauka. Zap. Nauchn. Semin. POMI. 221, 67-74 (1995). MSC: 35P25 35J05 78A45 PDF BibTeX XML OpenURL
Babich, V. M.; Samokish, B. A.; Demen’tev, D. B. Diffraction of a plane wave by a narrow cone. (English. Russian original) Zbl 0937.35513 J. Math. Sci., New York 87, No. 2, 3311-3315 (1997); translation from Zap. Nauchn. Semin. POMI 221, 67-74 (1995). MSC: 35P25 35J05 78A45 PDF BibTeX XML Cite \textit{V. M. Babich} et al., J. Math. Sci., New York 87, No. 2, 3311--3315 (1995; Zbl 0937.35513); translation from Zap. Nauchn. Semin. POMI 221, 67--74 (1995) Full Text: DOI OpenURL
Babich, V. M. Unique solvability of the Cauchy problem for a system of Maxwell equations with initial data on a timelike surface. (English. Russian original) Zbl 0870.35103 J. Math. Sci., New York 83, No. 2, 180-184 (1997); translation from Zap. Nauchn. Semin. POMI 210, 30-37 (1994). MSC: 35Q60 78A25 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 83, No. 1, 30--37 (1994; Zbl 0870.35103); translation from Zap. Nauchn. Semin. POMI 210, 30--37 (1994) Full Text: DOI EuDML OpenURL
Sabina, F. J.; Babich, V. M. Near and far scattering field of a low-frequency plane harmonic wave by a rough half-plane. (English) Zbl 0818.35075 Kleinman, Ralph (ed.) et al., Mathematical and numerical aspects of wave propagation. Proceedings of the 2nd international conference held in Newark, DE, USA, June 7-10, 1993. Philadelphia, PA: SIAM. 426-435 (1993). MSC: 35P25 78A45 35J05 PDF BibTeX XML Cite \textit{F. J. Sabina} and \textit{V. M. Babich}, in: Mathematical and numerical aspects of wave propagation. Proceedings of the 2nd international conference held in Newark, DE, USA, June 7-10, 1993. Philadelphia, PA: SIAM. 426--435 (1993; Zbl 0818.35075) OpenURL
Babich, V. M. Calculation of a “nongeometric” \(S^*\)-wave by using complex rays. (English. Russian original) Zbl 0836.73014 J. Math. Sci., New York 77, No. 3, 3146-3152 (1995); translation from Zap. Nauchn. Semi. POMI 200, 17-26 (1992). MSC: 74J10 78A05 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 77, No. 1, 17--26 (1992; Zbl 0836.73014); translation from Zap. Nauchn. Semi. POMI 200, 17--26 (1992) Full Text: DOI OpenURL
Babich, V. M. The calculation of a “non-geometrical” wave \(S^*\) by using complex rays. (Russian. English summary) Zbl 0811.73020 Zap. Nauchn. Semin. POMI 200, 17-26 (1992). Reviewer: D. Stanomir (Bucureşti) MSC: 74J10 78A05 PDF BibTeX XML Cite \textit{V. M. Babich}, Zap. Nauchn. Semin. POMI 200, 17--26 (1992; Zbl 0811.73020) Full Text: EuDML OpenURL
Babich, V. M. On applying complex rays to calculation of scalar “non-geometric” waves. (English. Russian original) Zbl 0835.73058 J. Math. Sci., New York 73, No. 3, 308-316 (1995); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 186, 20-32 (1990). MSC: 74F15 32A99 74J99 78A40 78A97 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Math. Sci., New York 73, No. 3, 20--32 (1990; Zbl 0835.73058); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 186, 20--32 (1990) Full Text: DOI OpenURL
Babich, V. M. The multidimensional WKB method or ray method. Its analogs and generalizations. (Russian) Zbl 0657.35119 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 34, 93-134 (1988). MSC: 35Q99 78A45 PDF BibTeX XML Cite \textit{V. M. Babich}, Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 34, 93--134 (1988; Zbl 0657.35119) OpenURL
Babich, V. M. The highest-dimensional WKB method or ray method. Its analogues and generalizations. (English. Russian original) Zbl 0907.35134 Partial differential equations V. Encycl. Math. Sci. 34, 91-131 (1999); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 34, 93-134 (1988). MSC: 35Q99 78A45 PDF BibTeX XML OpenURL
Babich, V. M. The application of Finsler geometry to the geometrical optics of nonhomogeneous anisotropic media. (English. Russian original) Zbl 0662.53023 Vestn. Leningr. Univ., Math. 20, No. 3, 9-14 (1987); translation from Vestn. Leningr. Univ., Ser. I 1987, No. 3, 19-23 (1987). MSC: 53B40 78A05 PDF BibTeX XML Cite \textit{V. M. Babich}, Vestn. Leningr. Univ., Math. 20, No. 3, 9--14 (1987; Zbl 0662.53023); translation from Vestn. Leningr. Univ., Ser. I 1987, No. 3, 19--23 (1987) OpenURL
Babich, V. M. Application of Finsler geometry to geometric optics of inhomogeneous anisotropic media. (Russian. English summary) Zbl 0633.53045 Vestn. Leningr. Univ., Ser. I 1987, No. 3, 19-23 (1987). Reviewer: V.Oproiu MSC: 53B40 78A05 PDF BibTeX XML Cite \textit{V. M. Babich}, Vestn. Leningr. Univ., Ser. I 1987, No. 3, 19--23 (1987; Zbl 0633.53045) OpenURL
Babich, V. M.; Smyshlyaev, V. P. The scattering problem for the Schrödinger equation with a potential linear in time and in space. II: Correctness, smoothness, behavior of the solution at infinity. (English) Zbl 0621.35076 J. Sov. Math. 38, 1562-1576 (1987). MSC: 35P25 35J10 78A45 35B40 35A05 35B65 PDF BibTeX XML Cite \textit{V. M. Babich} and \textit{V. P. Smyshlyaev}, J. Sov. Math. 38, 1562--1576 (1987; Zbl 0621.35076) Full Text: DOI OpenURL
Alekseev, A. S.; Babich, V. M. On the development of methods for problems of propagation and diffraction of waves by S. L. Sobolev. (Russian) Zbl 0638.35069 Partial differential equations, Proc. int. Conf., Novosibirsk 1983, 12-16 (1986). Reviewer: E.V.Nicolau MSC: 35Q99 35-03 78A45 74J20 78A40 01A60 PDF BibTeX XML OpenURL
Babich, V. M. The mathematical theory of diffraction ( a survey of some investigations carried out in the laboratory of mathematical problems of geophysics, Leningrad branch of the Mathematical Institute). (English. Russian original) Zbl 0850.01021 Proc. Steklov Inst. Math. 175, 47-63 (1988); translation from Tr. Mat. Inst. Steklova 175, 47-62 (1986). MSC: 01A74 35-02 35P25 78-02 78A45 PDF BibTeX XML Cite \textit{V. M. Babich}, Proc. Steklov Inst. Math. 175, 47--63 (1986; Zbl 0850.01021); translation from Tr. Mat. Inst. Steklova 175, 47--62 (1986) OpenURL
Babich, V. M. Skin-effect in the case of a conductor of an arbitrary cross section. (English) Zbl 0566.35087 J. Sov. Math. 30, 2373-2378 (1985). MSC: 35Q99 35C20 78A25 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Sov. Math. 30, 2373--2378 (1985; Zbl 0566.35087) Full Text: DOI OpenURL
Babich, V. M. The skin-effect in the case of a wire with arbitrary cross-section. (Russian. English summary) Zbl 0536.35071 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 128, 13-20 (1983). MSC: 35Q99 78A25 35C20 PDF BibTeX XML Cite \textit{V. M. Babich}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 128, 13--20 (1983; Zbl 0536.35071) Full Text: EuDML OpenURL
Babich, V. M. Focusing problem and the asymptotics of the spectral function of the Laplace-Beltrami operator. II. (English) Zbl 0495.35066 J. Sov. Math. 19, 1288-1322 (1982). MSC: 35P20 35B05 35J05 35P15 78A40 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Sov. Math. 19, 1288--1322 (1982; Zbl 0495.35066) Full Text: DOI OpenURL
Babich, V. M. A point source of oscillations near a concave mirror. II. (English) Zbl 0495.35005 J. Sov. Math. 19, 1279-1287 (1982). MSC: 35B05 35J05 35C10 78A40 PDF BibTeX XML Cite \textit{V. M. Babich}, J. Sov. Math. 19, 1279--1287 (1982; Zbl 0495.35005) Full Text: DOI OpenURL