The characteristic polynomial relation for the Navier system, in terms of frequencies and wavenumbers
**, will be
**

and has roots

Ignoring the non-propagating modes with frequency , and the multiplicities of the other modes, we can see that wave propagation is dispersionless, at least for the constant-coefficient problem. There are two wave speeds,

which are also known as the P-wave and S-wave (or compressional and shear wave) speeds [35].

For the varying-coefficient problem, the global maximum group velocity is then

Stefan Bilbao 2002-01-22