Thermo-electro-elastic waves in Pyroelectric media

There are 5 governing equations expressed by displacements, electric potential and temperature in Pyroelectric media, so the Christoffel character equation is a 5×5 matrix. But there are only 4 independent eigenvalues distinguished from zero for the wave propagated in an infinite homogenous space. The reflection and transmission problem is different from the wave propagation problem in an infinite space. In the reflection and transmission problem, the Christoffel character equation has 5 independent eigenvalues distinguished from zero because components of all wave vectors on the interface are equal due to the general Snell law. In the reflection and transmission problem there are 5 independent waves in each side of the interface, which may satisfy 10 continuous conditions at the interface.