On quasi-periodic solutions for a generalized Boussinesq equation

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.