Abstract:
In this paper, one-dimensional (1D) nonlinear wave equations
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 small-amplitude periodic or quasi-periodic 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 2 August 1999 / Accepted: 7 January 2000
Rights and permissions
About this article
Cite this article
Chierchia, L., You, J. KAM Tori for 1D Nonlinear Wave Equations¶with Periodic Boundary Conditions. Comm Math Phys 211, 497–525 (2000). https://doi.org/10.1007/s002200050824
Issue Date:
DOI: https://doi.org/10.1007/s002200050824