Quasi-periodic solutions for perturbed generalized KdV equation

We consider the generalized KdV equation ut=−uxxx+30u4uxut=−uxxx+30u4ux subject to periodic boundary conditions. We prove that the existence of many 2-dimensional invariant tori under sufficiently small Hamiltonian perturbations by means of infinite-dimensional KAM theory and partial Birkhoff normal form and thus many time quasi-periodic solutions for the above perturbed equation.