Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation (Q1811891)

The author investigates the existence of the inveriant tori of the nonlinear wave equation \[ u_{tt}=u_{xx}-V(x)u-f(u) \] with boundary conditions \[ u(t,0)=0=u(t,\pi),\;-\infty<t<+\infty, \] where the potential \(V\) is in the square-integrable function space \(L^2[0,\pi]\) and \(f\) is a real analytic, odd function of \(u\) of the form \[ f(u)=au^3+\sum_{k\geq 5}f_ku^k, a\not=0. \]