Quasi-periodic Solutions for Completely Resonant Quintic Beam Equations

This paper concerns the existence of quasi-periodic solutions for completely resonant quintic beam equations on one-dimensional tori. A novel Birkhoff normal form is developed to reformulate the problem into a nearly integrable system depending on the angle variables. The symplectic transformations, Floquet theory together with the averaging method are applied to reduce the influence of the angle variables. The proof is mainly based on an infinite-dimensional KAM theorem.

Automated summary

This paper discusses the existence of quasi-periodic solutions for completely resonant quintic beam equations on one-dimensional tori. A novel Birkhoff normal form is developed to reformulate the problem into a nearly integrable system depending on the angle variables. Symplectic transformations, Floquet theory, and the averaging method are utilized to reduce the influence of the angle variables. The proof mainly relies on an infinite-dimensional KAM theorem.