This work is devoted to the study of the system that arises by discretization of the periodic nonlinear Schrödinger equation in dimension one. We study the existence of the discrete ground states for this system and their stability property when the potential parameter ¾ is small enough: i.e., if the initial data are close to the ground state, the solution of the system will remain near to the orbit of the discrete ground state forever. This stability property is an appropriate tool for proving the convergence of the numerical method.
"Orbital stability of numerical periodi nonlinear Schrödinger equation." Commun. Math. Sci. 6 (1) 149 - 169, March 2008.