The novel class of exact solutions of the two-dimensional eikonal equation when the velocity in a medium depends on one spatial coordinate
E.D. Moskalensky
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
Keywords: распространение волн, фронт волны, уравнение эйконала, wave propagation, front of wave, eikonal equation
Abstract
The method to obtain solutions of the two-dimensional eikonal equation has been developed for the case when the velocity of wave propagation in a medium depends only on one spatial coordinate. We present several examples, where the initial problem is transformed to one or several ordinary differential equations using the substitution of the solution into a suitable general form. The dynamics of the wave propagation for each solution obtained is illustrated.
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