Email this article Simple Solutions of the Wave Equation with a Singularity at a Running Point, Based on the Complexified Bateman Solution
- Authors: Blagovestchenskii A.S.1, Kiselev A.P.2,3, Tagirdzhanov A.M.1
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Affiliations:
- St. Petersburg State University
- St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
- Institute of Mechanical Engineering RAS
- Issue: Vol 224, No 1 (2017)
- Pages: 47-53
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/239476
- DOI: https://doi.org/10.1007/s10958-017-3392-6
- ID: 239476
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Abstract
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.
About the authors
A. S. Blagovestchenskii
St. Petersburg State University
Author for correspondence.
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg
A. P. Kiselev
St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University; Institute of Mechanical Engineering RAS
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg
A. M. Tagirdzhanov
St. Petersburg State University; St. Petersburg State University
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg; St. Petersburg
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