PreprintCC BY 4.0arXiv
Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry
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.
Versions
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BibTeX
@misc{zarrinkamar2026algebraic,
title = {{Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry}},
author = {Saber Zarrinkamar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06657},
eprint = {2609.06657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06657},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry
AU - Saber Zarrinkamar
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06657
UR - https://arxiv.org/abs/2609.06657
AB - 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.
ER -