FINITE-ENERGY SOLUTION OF THE WAVE EQUATION THAT DOES NOT TEND TO A SPHERICAL WAVE AT INFINITY

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详细

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.

作者简介

A. Plachenov

MIREA — Russian Technological University

Email: a_plachenov@mail.ru
Moscow, Russia

A. Kiselev

St. Petersburg Department of Steklov Mathematical Institute of RAS; Institute of Mechanical Engineering of RAS

Email: aleksei.kiselev@gmail.com
St. Petersburg, Russia

参考

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

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