Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2

In the present paper, we consider two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Because of this reversible system without external parameters or potentials, Birkhoff normal form reduction is necessary before applying Kolmogorov-Arnold-Moser (KAM) theorem. As application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proved in this paper.

Automated summary

In this paper, we investigate two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Due to the absence of external parameters or potentials in this reversible system, Birkhoff normal form reduction is necessary before applying Kolmogorov-Arnold-Moser (KAM) theorem. As an application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proven.