Quasi-periodic solutions for perturbed generalized KdV equation. (December 2016) - Mi, Lufang; Zhang, Kangkang
Abstract: We consider the generalized KdV equation u t = − u x x x + 30 u 4 u x 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.