For the constant coefficient problem, the characteristic polynomial relating frequencies to spatial wavenumber
**, from (3.10), will be
**

The first factor, which is similar in form to that which defines the Timoshenko system, from (5.19), has four roots, , which behave as

and the second factor has a pair of roots , which have the limiting behavior

All phase and group velocities are thus bounded. For the varying-coefficient problem, the maximum global group velocity will be

Stefan Bilbao 2002-01-22