Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times
For researchers in nonlinear waves and discrete systems, this provides rigorous long-time stability results for discrete traveling waves, though the analysis is limited to the near-continuum regime.
The paper proves existence and long-time stability of traveling waves for the 1D discrete nonlinear Schrödinger equation near the continuous limit, using a modulation method to describe dynamics near these waves.
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous 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 also show that we can describe the dynamics near these discrete traveling waves over long times.