Quasi-periodic solutions for perturbed generalized KdV equation (Q2630067)

The authors consider the generalized Korteweg-de Vries (KdV) equation: \[ u_t=-u_{xxx}+30u^4u_x, \] subject to periodic boundary conditions. They prove the existence of many 2-dimensional invariant tori under sufficiently small Hamiltonian perturbations by means of infinite-dimensional Kolmogorov-Arnold-Moser (KAM) theory and partial Birkhoff normal form and thus of many time quasi-periodic solutions for the above perturbed equation.