EXISTENCE AND STABILITY OF TRAVELING WAVES FOR DISCRETE NONLINEAR SCHRODINGER EQUATIONS OVER LONG TIMES

摘要

We consider the problem of existence and stability of solitary traveling waves for the one-dimensional discrete nonlinear Schrodinger equation with cubic nonlinearity, near the continuum limit. We construct a family of solutions close to the continuous traveling waves and prove their stability over long times. Applying a modulation method, we describe the dynamics near these discrete traveling waves over long times.