Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times

Abstract

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.

References in corpus (2)

• Solitary Wave Dynamics in an External Potential
• Moving solitons in the discrete nonlinear Schrödinger equation

Cited by in corpus (1)

• Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schr{ö}dinger equations on $h\mathbb{Z}$