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

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.

Source: arXiv:2609.06657v1 - http://arxiv.org/abs/2609.06657v1 PDF: https://arxiv.org/pdf/2609.06657v1 Original Link: http://arxiv.org/abs/2609.06657v1