KAM for the nonlinear beam equation 1: small-amplitude solutions

Hakan L. Eliasson, Benoit Grebert, Sergei B. Kuksin

In this paper we prove a KAM result for the non linear beam equation on the d-dimensional torus $$u_{tt}+Δ^2 u+m u + g(x,u)=0\ ,\quad t\in { \mathbb{R}} , \; x\in {\mathbb T}^d, \q…