Quasi-periodic solutions for perturbed generalized KdV equation. (December 2016)

• Record Type: Journal Article
• Authors: Mi, Lufang; Zhang, Kangkang
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 314
• Page End: 337
• Publication Date: 2016-12
• Subjects: Generalized KdV equation -- KAM theory -- Birkhoff normal form -- Quasi-periodic solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.05.003
• Languages: English
• ISSNs: 1468-1218

Abstract

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.