Long time stability of KAM tori for the generalized Boussinesq equation. (November 2020)

• Record Type: Journal Article
• Authors: Wang, Shimin; Lou, Zhaowei; Si, Jianguo
• Is Part Of: Nonlinear analysis. Volume 200(2020)
• Publication Date: 2020-11
• Subjects: KAM tori -- Long time stability -- p-tame property -- Generalized Boussinesq equation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.112084
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove that the KAM tori for the generalized Boussinesq equation with the external parameters, which generates an infinite dimensional Hamiltonian system, are long-time stable. Precisely, we prove that the solutions with initial datum in the δ -neighborhood of KAM torus still stay close to the KAM torus for | t | ≤ δ − M with M ≥ 1 . The proof is based on constructing a partial normal form of higher order and showing that the p -tame property for the Hamiltonian vector field persists after the changes of variables of the KAM scheme and under normal form iterative procedure.