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A Family of Solutions to the Two-Dimensional Eikonal Equation

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ABSTRACT

The propagation of a wave from a point source when the velocity \(v\) in the medium is expressed as \(v = \frac {1}{\sqrt y}\) is considered. Exact solutions to the corresponding eikonal equation are obtained and numerically verified. It is shown that the solution of this equation when the point source is at the origin of coordinates is not unique.

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REFERENCES

  1. Smirnov, V.I., A Course of Higher Mathematics, vols. 1–5, New York: Pergamon Press, 1964.

  2. Moskalensky, E.D., A New Class of Exact Solutions to the Two-Dimensional Eikonal Equation where the Velocity in the Medium Depends on One of the Spatial Coordinates Alone, Sib. Zh. Vych. Mat., 2018, vol. 21, no. 3, pp. 259–271.

  3. Borovskikh, A.V., Two-Dimensional Eikonal Equation, Sib. Mat. Zh., 2006, vol. 47, no. 5, pp. 993–1018.

  4. Marchuk, An.G., Minimizing Errors in Numerical Calculations of Wave Rays and Tsunami Fronts, Vestnik NGU, Ser. Inform. Tekhnol., 2013, vol. 11, no. 3, pp. 27–36.

  5. Stocker, J.J., Water Waves: The Mathematical Theory with Applications, New York: Interscience, 1957.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    An. G. Marchuk & E. D. Moskalensky

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  1. An. G. Marchuk
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  2. E. D. Moskalensky
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Correspondence to An. G. Marchuk or E. D. Moskalensky.

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Marchuk, A.G., Moskalensky, E.D. A Family of Solutions to the Two-Dimensional Eikonal Equation. Numer. Analys. Appl. 13, 127–135 (2020). https://doi.org/10.1134/S1995423920020044

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  • DOI: https://doi.org/10.1134/S1995423920020044

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