Finding exact solutions to the two-dimensional eikonal equation |
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| Authors: | E D Moskalensky |
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| Institution: | 1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia
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| Abstract: | A two-dimensional eikonal equation f x 2 + f y 2 = ? 2, where ? = 1/υ and υ(x, y) is the wave propagation velocity, is discussed. This nonlinear equation is reduced to a quasilinear equation for a new dependent variable u. Solutions to quasilinear equations are found for some kinds of functions ?. Hence, the original equation can well be solved for such ?. An approach to finding a new solution based on a known one is proposed. |
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