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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 2, Pages 201–209
(Mi sjvm16)
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This article is cited in 5 scientific papers (total in 5 papers)
Finding exact solutions to the two-dimensional eikonal equation
E. D. Moskalenskii Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
Abstract:
In this paper, the two-dimensional eikonal equation $f_x^2+f_y^2=\phi^2$, where $\phi=\frac1{v}$, and $v(x,y)$ is a wavespropagation velocity, is discussed. This non-linear equation is reduced to a quasilinear equation for a new dependent variable $u$. For some kinds of the functions $\phi$, solutions to the quasilinear equations are found. This means that it is possible to solve the original equation for such $\phi$. This paper also offers an approach to finding a new solution based on a known one.
Key words:
wave propagation, inhomogeneous medium, eikonal equation, harmonic functions.
Received: 11.08.2008
Citation:
E. D. Moskalenskii, “Finding exact solutions to the two-dimensional eikonal equation”, Sib. Zh. Vychisl. Mat., 12:2 (2009), 201–209; Num. Anal. Appl., 2:2 (2009), 165–172
Linking options:
https://www.mathnet.ru/eng/sjvm16 https://www.mathnet.ru/eng/sjvm/v12/i2/p201
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Abstract page: | 573 | Full-text PDF : | 232 | References: | 46 | First page: | 11 |
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