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March  2006, 16(1): 227-234. doi: 10.3934/dcds.2006.16.227

The existence of integrable invariant manifolds of Hamiltonian partial differential equations

Rongmei Cao 1, and  Jiangong You 2,

1. 

College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2. 

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  July 2005 Revised  January 2006 Published  June 2006

In this note, it is shown that some Hamiltonian partial differential equations such as semi-linear Schrödinger equations, semi-linear wave equations and semi-linear beam equations are partially integrable, i.e., they possess integrable invariant manifolds foliated by invariant tori which carry periodic or quasi-periodic solutions. The linear stability of the obtained invariant manifolds is also concluded. The proofs are based on a special invariant property of the considered equations and a symplectic change of variables first observed in [26].
Keywords: Integrability, Hamiltonian PDEs, KAM theorem..
Mathematics Subject Classification: Primary 37K55, 35Q5.
Citation: Rongmei Cao, Jiangong You. The existence of integrable invariant manifolds of Hamiltonian partial differential equations. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 227-234. doi: 10.3934/dcds.2006.16.227
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