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ЖУРНАЛЫ // Записки научных семинаров ПОМИ

Зап. научн. сем. ПОМИ, 2018, том 471, страницы 76–85 (Mi znsl6625)

On the Bateman–Hörmander solution of the wave equation, having a singularity at a running point
A. S. Blagoveshchensky, A. M. Tagirdzhanov, A. P. Kiselev

Литература

1. L. Hörmander, The Analysis of Linear Partial Differential Operators, v. I, Distribution Theory and Fourier Analysis, Springer, Berlin, 1983  mathscinet  zmath
2. H. Bateman, “The conformal transformations of space of four dimensions and their applications to geometrical optics”, Proc. London Math. Soc., 7 (1909), 70–89  crossref  mathscinet  zmath
3. H. Bateman, The Mathematical Analysis of Electrical and OpticalWave-Motion on the Basis of Maxwell's Equations, Dover, NY, 1955  mathscinet
4. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Pergamon, Oxford, 1971  mathscinet
5. P. Hillion, “The Courant–Hilbert solutions of the wave equation”, J. Math. Phys., 33:8 (1992), 2749–2753  crossref  mathscinet  zmath  adsnasa
6. A. P. Kiselev, M. V. Perel, “Highly localized solutions of the wave equation”, J. Math. Phys., 41:4 (2000), 1934–1955  crossref  mathscinet  zmath  adsnasa
7. A. P. Kiselev, “Localized light waves: Paraxial and exact solutions of the wave equation (a review)”, Optics and Spectroscopy, 102:4 (2007), 603–622  crossref  adsnasa
8. I. M. Besieris, A. M. Shaarawi, A. M. Attiya, “Bateman conformal transformations within the framework of the bidirectional spectral representation”, Progress in Electromagnetics Research, 48 (2004), 201–231  crossref
9. A. P. Kiselev, A. B. Plachenov, “Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalizations of the Bateman solution”, J. Math. Sci., 185:4 (2012), 605–610  mathnet  crossref  mathscinet  zmath
10. V. S. Vladimirov, Equations of Mathematical Physics, Mir, Moscow, 1985  mathscinet
11. A. S. Blagoveshchensky, “Plane waves, Bateman's solutions, and sources at infinity”, J. Math. Sci., 214:3 (2016), 260–267  mathnet  crossref  mathscinet  zmath
12. A. S. Blagovestchenskii, A. P. Kiselev, A. M. Tagirdzhanov, “Simple solutions of the wave equation with a singularity at a running point, pased on the complexified Bateman solution”, J. Math. Sci., 224:1 (2017), 47–53  mathnet  crossref  mathscinet  zmath


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