arXiv subjects
Publications and source records attributed to Xindong Xu.
We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schrödinger equation with quasi-periodic time-dependent forcing.
Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schrödinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean frequency.
We define and describe the class of Quasi-Töplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scrödinger equation on the torus $T^d$, thus proving existence and stability of quasi-periodic solutions and recovering the results of [10]. With respect to that paper we consider only the NLS which preserves the total Momentum and exploit this conserved quantity in order to simplify our treatment.