We consider Hamiltonian partial differential equations utt ＋ ｜δx｜u ＋ σu = f（u）, x ∈T, t ∈R, with periodic boundary conditions, where f（u） is a real-analytic function of the form f（u） = u5 ＋ σ（u5） nea...We consider Hamiltonian partial differential equations utt ＋ ｜δx｜u ＋ σu = f（u）, x ∈T, t ∈R, with periodic boundary conditions, where f（u） is a real-analytic function of the form f（u） = u5 ＋ σ（u5） near u = 0, σ ∈（0, 1） is a fixed constant, and T = R/2πZ. A family of quasi-periodic solutions with 2-dimensional are constructed for the equation above with σ ∈ （0, 1）Q. The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form.展开更多
文摘We consider Hamiltonian partial differential equations utt ＋ ｜δx｜u ＋ σu = f（u）, x ∈T, t ∈R, with periodic boundary conditions, where f（u） is a real-analytic function of the form f（u） = u5 ＋ σ（u5） near u = 0, σ ∈（0, 1） is a fixed constant, and T = R/2πZ. A family of quasi-periodic solutions with 2-dimensional are constructed for the equation above with σ ∈ （0, 1）Q. The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form.
