Stability and interaction of compactons in the sublinear KdV equation

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 propor...

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Bibliographic Details
Published inarXiv.org
Main Authors Pelinovsky, Dmitry E, Slunyaev, Alexey V, Kokorina, Anna V, Pelinovsky, Efim N
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.01.2021
Subjects
Korteweg-Devries equation
Mathematics - Analysis of PDEs
Mathematics - Dynamical Systems
Mathematics - Mathematical Physics
Physics - Exactly Solvable and Integrable Systems
Physics - Mathematical Physics
Physics - Pattern Formation and Solitons
Polarity
Solitary waves
Stability
Wave power
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.02816