Abstract
The filtration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modified asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coefficients of expansion in an asymptotic parameter. The zero expansion coefficient describes the sought plane wave, whereas the first coefficient ensures refinement of the wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confirmed by comparing the obtained asymptotic solutions and the coefficients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
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