Construction of quasi-periodic solutions for nonlinear forced perturbations of dissipative Boussinesq systems. (October 2022)

• Record Type: Journal Article
• Authors: Zhang, Yuan; Si, Wen; Si, Jianguo
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Dissipative Boussinesq systems -- KAM for PDEs -- Nash–Moser iterative scheme -- Quasi-periodic solutions -- Hamiltonian and reversible systems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103621
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we consider a class of quasi-periodically forced perturbations of the dissipative Boussinesq systems with an elliptic fixed point (see (1.4) ) in two cases: Hamiltonian case and reversible case. We prove the existence and linear stability of quasi-periodic solutions for the system (1.4) with periodic boundary conditions. The method of proof is based on a Nash–Moser iterative scheme in the scale of Sobolev spaces developed by Berti and Bolle in Berti and Bolle (2013, 2012), but we have to be substantially developed to deal with the system (1.4) considered here.