The existence of integrable invariant manifolds of Hamiltonian partial differential equations

Rongmei Cao; Jiangong You

doi:10.3934/dcds.2006.16.227

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2006, Volume 16, Issue 1: 227-234. Doi: 10.3934/dcds.2006.16.227

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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
2.
Department of Mathematics, Nanjing University, Nanjing 210093

Received: July 2005

Revised: January 2006

Published: March 2006

Abstract / Introduction Related Papers Cited by

Abstract

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].

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Mathematics Subject Classification: Primary 37K55, 35Q55.

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