D.E. Pelinovsky, A.V. Slunyaev, A.V. Kokorina, and E.N. Pelinovsky
Stability and interaction of compactons in the sublinear KdV equation
Commun Nonlinear Sci Numer Simulat 101 (2021) 105855 (16 pages)
Abstract:
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 solitonlike
structures and of the small-scale waves which spread the wave energy.
Keywords:
Sublinear Korteweg-de Vries equation, compactons, existence and stability, interactions.