  Compactons are studied in the framework of the Korteweg-de Vries (KdV)
equation with the sublinear nonlinearity. Compactons represent localized
bell-shaped waves of either polarity which propagate to the same direction as
waves of the linear KdV equation. Their amplitude and width are inverse
proportional to their speed. The energetic stability of compactons with respect
to symmetric compact perturbations with the same support is proven
analytically. Dynamics of compactons is studied numerically, including
evolution of pulse-like disturbances and interactions of compactons of the same
or opposite polarities. Compactons interact inelastically, though almost
restore their shapes after collisions. Compactons play a two-fold role of the
long-living soliton-like structures and of the small-scale waves which spread
the wave energy.
