  We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de
Vries (KdV) evolution equations based on a modification of the Lagrangian
density whose induced action functional the KdV equation extremizes. It is
shown that two recent nonlinear evolution equations describing wave propagation
in certain generalized continua with an inherent material length scale are
members of the proposed hierarchy. Like KdV, the equations from the proposed
hierarchy possess Hamiltonian structure. Unlike KdV, however, the solutions to
these equations can be compact (i.e., they vanish outside of some open
interval) and, in addition, peaked. Implicit solutions for these peaked,
compact traveling waves ("peakompactons") are presented.
