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Geng, Jiansheng; You, Jiangong

A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces. (English) Zbl 1103.37047

Commun. Math. Phys. 262, No. 2, 343-372 (2006).
Summary: We give a KAM theorem for a class of infinite-dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher-dimensional spaces with periodic boundary conditions to construct linearly stable quasi-periodic solutions and its local Birkhoff normal form. The applications to the higher-dimensional beam equations and the higher-dimensional Schrödinger equations with nonlocal smooth nonlinearity are given in this paper, too.

Cited in 1 Review
Cited in 115 Documents

MSC:

37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
35Q72 Other PDE from mechanics (MSC2000)
35Q55 NLS equations (nonlinear Schrödinger equations)
35L75 Higher-order nonlinear hyperbolic equations

Keywords:

infinite-dimensional nearly integrable Hamiltonian systems; quasi-periodic solutions; Birkhoff normal form; higher-dimensional beam equations; higher-dimensional Schrödinger equations
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References:

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