  We derive a general theorem relating the energy, momentum and velocity of any
solitary wave solution of the generalized KdV equation which enables us to
relate the amplitude, width, and momentum to the velocity of these solutions.
We obtain the general condition for linear and Lyapunov stability. We then
obtain a two parameter family of exact solutions to these equations which
include elliptic and hyper-elliptic compacton solutions. For this general
family we explicitly verify both the theorem and the stability criteria.

Pattern Formation and Solitons;Exactly Solvable and Integrable Systems