Resumen de Quasi-Periodic Solutions for Two Dimensional Generalized Boussinesq Equation with Higher Order Nonlinearity

Yanling Shi

• In this paper, two dimensional generalized Boussinesq equation utt − u + 2u + (u5) = 0, x ∈ T2, t ∈ R under 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, partial Birkhoff normal form and scaling skills.