Arnold diffusion of the discrete nonlinear Schrödinger equation (Q851469)

The goal of this paper is to study in detail the discrete nonlinear Schrödinger equation (DNLS) and its continuous version, the nonlinear Schrödinger equation (NLS). DNLS is an integrable finite difference discretization of NLS. An interesting fact about DNLS is that one can choose and change the dimensions of the phase space by selecting the number of particles in the discretizations. For a two-particle case, under periodic Hamiltonian perturbations, the resulting system is 5-dimensional, for which the author proves the existence of Arnold diffusion.