Long time stability of KAM tori for nonlinear wave equation (Q2259255)

The authors consider the nonlinear wave equation of the form \[ u_{tt}-u_{xx}+V(x)u +u^3 +h.o.t.=0 \] subject to the Dirichlet boundary conditions \(u(t,0)=u(t,\pi)=0\). It is shown that KAM tori for this infinite dimensional Hamiltonian system are long time stable. The proof relies on a construction of partial normal form around the KAM torus, and persistence of the so-called \(p\)-tame property under KAM iterations and normal form iterations.