Email this article 
FINITE-ENERGY SOLUTION OF THE WAVE EQUATION THAT DOES NOT TEND TO A SPHERICAL WAVE AT INFINITY
- Authors: Plachenov A.B1, Kiselev A.P2,3
-
Affiliations:
- MIREA — Russian Technological University
- St. Petersburg Department of Steklov Mathematical Institute of RAS
- Institute of Mechanical Engineering of RAS
- Issue: Vol 60, No 11 (2024)
- Pages: 1562-1565
- Section: BRIEF MESSAGES
- URL: https://ter-arkhiv.ru/0374-0641/article/view/649595
- DOI: https://doi.org/10.31857/S0374064124110113
- EDN: https://elibrary.ru/JDQMIZ
- ID: 649595
Cite item
Open Access
Access granted
Subscription Access
Abstract
A solution of the wave equation with three spatial variables is given, which has a finite energy integral, but does not tend to a spherical wave at infinity.
Keywords
About the authors
A. B Plachenov
MIREA — Russian Technological University
Email: a_plachenov@mail.ru
Moscow, Russia
A. P Kiselev
St. Petersburg Department of Steklov Mathematical Institute of RAS; Institute of Mechanical Engineering of RAS
Email: aleksei.kiselev@gmail.com
St. Petersburg, Russia
References
- Blagoveshchenskii, A.S. On some new correct problems for the wave equation, in: Proc. 5th All-Union Symp. on Wave Diffr. Propag., Leningrad: Nauka, 1971, pp. 29–35.
- Moses, R.N. Acoustic and electromagnetic bullets: derivation of new exact solutions of the acoustic and Maxwell’s equations / R.N. Moses, H.E. Prosser // SIAM J. Appl. — 1990. — V. 50, № 5. — P. 1325-1340.
- Blagoveshchenskii, A.S. and Novitskaya, A.A., On behavior of the solution of a generalized Cauchy problem for the wave equation at infinity, J. Math. Sci. (N.Y.), 2004, vol. 122, no. 5, pp. 3470–3472.
- Kiselev, A.P., Localized light waves: paraxial and exact solutions of the wave equation (a review), Optics and Spectroscopy, 2007, vol. 102, no. 4, pp. 603–622.
- Friedlander, F.G. On the radiation field of pluse solution of the wave equation. II / F.G. Friedlander // Proc. Roy. Soc. London, Ser. A, Math. Phys. Sci. — 1964. — V. 279, № 1378. — P. 386-394.
- Plachenov, A.B., Energy of waves (acoustic, electromagnetic, elastic) via their far-field asymptotics at large time, J. Math. Sci. (N.Y.), 2023, vol. 277, no. 4, pp. 653–665.
- Plachenov, A.B. and Kiselev, A.P., Unidirectional pulses: relatively undistorted quasi-spherical waves, Fourier–Bessel integrals, and plane-waves decompositions, Optics and Spectroscopy, 2024, vol. 132, no. 4, pp. 394–398.
- Ziolkowski, R.W. Exact solutions of the wave equation with complex source locations / R.W. Ziolkow-sky // J. Math. Phys. — 1985. — V. 26, № 4. — P. 861-863.
Supplementary files
