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Литература
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1. |
L. Hörmander, The Analysis of Linear Partial Differential Operators, v. I, Distribution Theory and Fourier Analysis, Springer, Berlin, 1983 |
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 |
3. |
H. Bateman, The Mathematical Analysis of Electrical and OpticalWave-Motion on the Basis of Maxwell's Equations, Dover, NY, 1955 |
4. |
L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Pergamon, Oxford, 1971 |
5. |
P. Hillion, “The Courant–Hilbert solutions of the wave equation”, J. Math. Phys., 33:8 (1992), 2749–2753 |
6. |
A. P. Kiselev, M. V. Perel, “Highly localized solutions of the wave equation”, J. Math. Phys., 41:4 (2000), 1934–1955 |
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 |
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 |
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 |
10. |
V. S. Vladimirov, Equations of Mathematical Physics, Mir, Moscow, 1985 |
11. |
A. S. Blagoveshchensky, “Plane waves, Bateman's solutions, and sources at infinity”, J. Math. Sci., 214:3 (2016), 260–267 |
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 |