弹性SH波在各向同性非均匀几何体中传播的代数解
Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry
- Universidad de Valladolid（巴利亚多利德大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文发现弹性SH波在各向同性非均匀层中传播问题具有隐藏的sl(2)对称性，从而通过解析方法获得准精确解，并可将方法推广至其他几何体。
AI中文摘要：
本文重新审视了控制弹性SH波在由两个均匀半空间包围的各向同性非均匀层中传播的方程代数结构。研究表明，在四次变化下，该问题具有隐藏的sl(2)对称性，基于此对称性，通过完全解析的方法可获得准精确解。这一点尤为重要，因为针对相应的三合流Heun方程所提出的方法也可推广到其他类别的几何体，并且避免了Heun方程情形下复杂的考量。
英文摘要：
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.
