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Quasi-periodic Solutions for 2k Order Wave Equations
Gao Yixian 1 *,Chang Jing 2
1.College of Mathematics and Statistics, Northeast Normal University
2.Fundamental Department, Aviation University of Air Force
*Correspondence author
#Submitted by
Funding: SRFDP(No.Grant 20100043120001), NSFC (No.Grant 11001042), Science Foundation for Young Teachers of North-east Normal University(No.09QNJJ002)
Opened online:29 March 2011
Accepted by: none
Citation: Gao Yixian,Chang Jing.Quasi-periodic Solutions for 2k Order Wave Equations[OL]. [29 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4417792
In this paper, we consider one-dimensional (1D) nonlinear 2k order wave equations under the Dirichlet boundary conditions, weher the nonlinearity f is an analytic, odd function. It is proved that for almost all real pa-rameters m>0, the equations admit small-amplitude quasi-periodic solutionscorresponding to finite dimensional invariant tori for an associated infnite dimensional dynamical system. The proof is based on an infnite dimensional KAM theory and apartial Birkhoff normal form technique.
Keywords: 2k order wave equations; KAM theory; Quasi-periodic solutions; Partial Birkhoff normal form

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