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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

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Abstract

A new method to obtain exact solutions to the two-dimensional eikonal equation where the velocity of the medium depends on one of the spatial coordinates alone is proposed. Several examples of reducing the initial problem to one or several ordinary differential equations by substituting the solution into a suitable general form are presented. The dynamics of wave propagation is illustrated for each of the solutions thus obtained.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Marchuk, An.G., Chubarov, L.B., and Shokin, Yu.I., Chislennoe modelirovanie voln tsunami (Numerical Simulation of TsunamiWaves), Novosibirsk: Nauka, 1983.

    MATH  Google Scholar 

  3. Marchuk, An.G., Estimating Tsunami Wave Height over a Sloping Bottom in the Ray Approximation, Sib. Zh. Vych. Mat., 2015, vol. 18, no. 4, pp. 377–388.

    MATH  Google Scholar 

  4. Marchuk, An.G., Estimating the Height of a TsunamiWave Propagating over a Parabolic Bottom in the Ray Approximation, Sib. Zh. Vych. Mat., 2017, vol. 20, no. 1, pp. 23–35.

    MATH  Google Scholar 

  5. Filippov, A.T., Mnogolikii soliton (The Versatile Soliton), Moscow: Nauka, 1986.

    Google Scholar 

  6. Moskalensky, E.D., On Detecting a Wavefront Described by a 2D Eikonal Equation when the Velocity in the Medium Depends on One Spatial Variable, Sib. Zh. Vych. Mat., 2010, vol. 13, no. 1, pp. 67–73.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    E. D. Moskalensky

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  1. E. D. Moskalensky
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Correspondence to E. D. Moskalensky.

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Original Russian Text © E.D. Moskalensky, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 3, pp. 259–271.

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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. Numer. Analys. Appl. 11, 208–219 (2018). https://doi.org/10.1134/S1995423918030035

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  • DOI: https://doi.org/10.1134/S1995423918030035

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