Abstract
A relation between two previously known exact solutions of the wave equation that describe propagation of localized waves is found.
Similar content being viewed by others
References
Localized Waves, Ed. by H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami (Wiley-VCH, Berlin, 2013).
A. M. Tagirdzhanov and A. P. Kiselev, “Complexified spherical waves and their sources: A review,” Opt. Spectrosc. 119 (2), 661–681 (2015).
C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: A scalar treatment,” Phys. Rev. A 57 (4), 2971–2979 (1998).
A. M. Tagirdzhanov, A. S. Blagovestchenskii, and A. P. Kiselev, “Complex source’ wavefields: Sources in real space,” J. Phys. A 44 (42), 425203 (2011).
P. Hillion, “The Courant–Hilbert solutions of the wave equation,” J. Math. Phys. 33 (8), 2749–2753 (1992).
E. Heyman and L. B. Felsen, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6 (6), 806–817 (1989).
A. S. Blagovestchenskii, A. P. Kiselev, and A. M. Tagirdzhanov, “Simple solutions of the wave equation, with a singularity at a moving point, based on the complexified Bateman solution,” J. Math. Sci. 224 (1), 47–53 (2017).
L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. 1: Distribution Theory and Fourier Analysis (Springer-Verlag, Berlin, 1983; Mir, Moscow, 1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.S. Blagoveshchensky, A.P. Kiselev, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 6, pp. 958–960.
Rights and permissions
About this article
Cite this article
Blagoveshchensky, A.S., Kiselev, A.P. A relation between two simple localized solutions of the wave equation. Comput. Math. and Math. Phys. 57, 953–955 (2017). https://doi.org/10.1134/S0965542517060057
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542517060057