Two-dimensional non-linear evolution equations: The derivation and the transient wave solution |
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Authors: | J. Engelbrecht |
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Affiliation: | Department of Engineering Mathematics, The University, Newcastle upon Tyne, U.K. |
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Abstract: | The general theory of two-dimensional evolution equations describing transient wave propagation in non-linear continuous media is presented. The ray method is used and the two-dimensional evolution equations for plane and cylindrical wave-beams are obtained. The transient wave solutions are discussed briefly. A transformation of variables is proposed that permits the transformation of the two-dimensional evolution equation into a one-dimensional evolution equation with coordinate-dependent coefficients. A breakdown time analysis is carried out for this case. The dispersion relations for plane and cylindrical wave-beams are presented. The non-linear dispersion relation is obtained by making use of a series representation. |
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