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

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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.

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

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  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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