  In this paper, we study the orbital stability for a four-parameter family of
periodic stationary traveling wave solutions to the generalized Korteweg-de
Vries equation. In particular, we derive sufficient conditions for such a
solution to be orbitally stable in terms of the Hessian of the classical action
of the corresponding traveling wave ordinary differential equation restricted
to the manifold of periodic traveling wave solution. We show this condition is
equivalent to the solution being spectrally stable with respect to
perturbations of the same period in the case of the Korteweg-de Vries equation,
and in neighborhoods of the homoclinic and equilibrium solutions in the case of
a power-law nonlinearity.
