Special features of the KdV-Sawada-Kotera equation

dc.creatorZarmi, Yair
dc.date2008-12-02
dc.date.accessioned2026-07-07T12:08:40Z
dc.date.available2026-07-07T12:08:40Z
dc.descriptionThe KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed KdV equation, the asymptotic expansion of the solution is developed through third order within the framework of a Normal Form analysis. It is shown that the equation is asymptotically integrable through the order considered. Focusing on the soliton sector, it is shown that the higher-order corrections in the Normal Form expansion represent purely inelastic KdV-soliton-collision processes, and vanish identically in the single-soliton limit. These characteristics are satisfied by the exact two-soliton solution of the KdV-Sawada-Kotera equation: The deviation of this solution from its KdV-type two-soliton approximation describes a purely inelastic scattering process: The incoming state is the faster KdV soliton. It propagates until it hits a localized perturbation, which causes its transformation into the outgoing state, the slower soliton. In addition, the effect of the perturbation on the exact two-soliton solution vanishes identically in the single-soliton limit (equal wave numbers for the two solitons).
dc.description15 pages, 2 figured
dc.identifierhttps://arxiv.org/abs/0812.0568
dc.identifierhttp://arxiv.org/abs/0812.0568
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209400
dc.subjectExactly Solvable and Integrable Systems
dc.titleSpecial features of the KdV-Sawada-Kotera equation
dc.typetext

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