Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry

Saber Zarrinkamar

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arXiv · 2609.06657

Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry

Saber Zarrinkamar

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Abstract

The algebraic structure of the equation governing the propagation of an elastic SHwave through an isotropic inhomogeneous layer surrounded by two homogeneous half-spaces is revisited. It is shown that the problem under a quartic variation has a hidden sl(2) symmetry based on which quasi-exact solutions are available via a completely analytical approach. This is of particular interest as the approach proposed for the corresponding tri-confluent Heun equation can be generalized to some other classes of geometries as well and the complicated considerations in case of Heun equations are absent.

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Saber Zarrinkamar. 2026-09-06. Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry. https://arxiv.org/abs/2609.06657

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