KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions
Abstract
In this paper, onedimensional (1D) nonlinear wave equations<FORMULA FORM="DISPLAY" DISC="MATH"> with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits smallamplitude periodic or quasiperiodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/s002200050824
 arXiv:
 arXiv:chaodyn/9904036
 Bibcode:
 2000CMaPh.211..497C
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 30 pages