Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839860 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 12 Pages |
Abstract
In this paper a one-dimensional generalized Boussinesq equation utt−uxx+(u3+uxx)xx=0utt−uxx+(u3+uxx)xx=0 with hinged boundary conditions is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on an infinite dimensional KAM theorem and the Birkhoff normal form.
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Authors
Yanling Shi, Junxiang Xu, Xindong Xu,