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Simple Solutions of the Wave Equation with a Singularity at a Running Point, Based on the Complexified Bateman Solution

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Simple explicit solutions of the homogeneous wave equation with constant propagation speed, having a power-like singularity at a moving space point, are constructed. The constructions are based on a complexified Bateman-type solution. An example of such a solution showing exponential decay with distance from the singular point is presented.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. S. Blagovestchenskii & A. M. Tagirdzhanov

  2. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University; Institute of Mechanical Engineering RAS, St. Petersburg, Russia

    A. P. Kiselev

  3. St. Petersburg State University, St. Petersburg, Russia

    A. M. Tagirdzhanov

Authors
  1. A. S. Blagovestchenskii
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  2. A. P. Kiselev
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  3. A. M. Tagirdzhanov
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Corresponding author

Correspondence to A. S. Blagovestchenskii.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 438, 2015, pp. 73–82.

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Blagovestchenskii, A.S., Kiselev, A.P. & Tagirdzhanov, A.M. Simple Solutions of the Wave Equation with a Singularity at a Running Point, Based on the Complexified Bateman Solution. J Math Sci 224, 47–53 (2017). https://doi.org/10.1007/s10958-017-3392-6

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  • DOI: https://doi.org/10.1007/s10958-017-3392-6

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