INVARIANT TORI FOR THE HAMILTONIAN DERIVATIVE WAVE EQUATION WITH HIGHER ORDER NONLINEARITY

In this paper, we will study the Hamiltonian derivative wave equation with higher order nonlinearity ytt - yxx + my + (Dy)(5) = 0, x is an element of T :- R/2 pi Z, where m > 0 is a potential and D := root -partial derivative xx + m. We will prove that, for any integer b >= 2, the above equation admits many small amplitude quasi-periodic solutions corresponding to b -dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on infinite dimensional KAM theory and partial Birkhoff normal form.