Hermite-Gaussian beams in a 3-D inhomogeneous elastic medium are derived as the high-frequency asymptotic solutions of the elastodynamic equations, concentrated close to the rays of P and S waves. In this case, the elastodynamic equations are reduced to the parabolic (Schroedinger) equation. The explicite expressions for the complete system of linearly independent solutions of the parabolic equation are presented. The derivation takes advantage of the method of ladder operators known from the quantum mechanics.
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