Data di Pubblicazione:
2009
Citazione:
Invariant tori for commuting Hamiltonian PDEs / D. Bambusi, C. Bardelle. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 246:6(2009 Mar 15), pp. 2484-2505.
Abstract:
We generalize to some PDEs a theorem by Eliasson and Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with r integrals of motion and n degrees of freedom, rn. The result we get ensures the persistence of an r-parameter family of r-dimensional invariant tori. The parameters belong to a Cantor-like set. The proof is based on the Lyapunov–Schmidt decomposition and on the standard implicit function theorem. Some of the persistent tori are resonant. We also give an application to the nonlinear wave equation with periodic boundary conditions on a segment and to a system of coupled beam equations. In the first case we construct 2-dimensional tori, while in the second case we construct 3-dimensional tori.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
quasi-periodic solutions; nonlinear-ware equations; perturbations; systems; 1D; 2D
Elenco autori:
D. Bambusi, C. Bardelle
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