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Construction of quasi-periodic solutions for nonlinear forced perturbations of dissipative Boussinesq systems |
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| Institution: | 1. School of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China;2. School of Mathematics, Sichuan University. Chengdu, Sichuan 610064, PR China;1. School of Mathematics and Statistics & Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, Jiangsu 221000, PR China;2. School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China |
| 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. |
| Keywords: | Dissipative Boussinesq systems KAM for PDEs Nash–Moser iterative scheme Quasi-periodic solutions Hamiltonian and reversible systems |
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