Stability and interaction of compactons in the sublinear KdV equation

• Published in: Communications in nonlinear science & numerical simulation Vol. 101; p. 105855
• Main Authors: Pelinovsky, Dmitry E., Slunyaev, Alexey V., Kokorina, Anna V., Pelinovsky, Efim N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2021; Elsevier Science Ltd
• Subjects: Compactons; Korteweg-Devries equation; Nonlinear equations; Perturbation; Propagation; Schrodinger equation; Solitary waves; Stability; Stability and interaction; Studies; Sublinear Korteweg-de Vries equation; Surface waves; Wave power; Sublinear Korteweg-de Vries equation; Compactons; Stability and interaction
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2021.105855

•We study compactons in 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.•We show the energetic stability of compactons with respect to symmetric compact perturbations with the same support.•We simulate dynamics of compactons 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. 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.