In this paper, two dimensional modified Boussinesq equationu(tt)+Delta(2)u+Delta(u(3))=0, x is an element of T-2, t is an element of Runder periodic boundary conditions is considered. It is proved that the above equation admits a Whitney smooth family of 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 Birkhoff normal form.
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