Stability of periodic optical solitons for a nonlinear Schrödinger system

Abstract

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrödinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minimal period. We also establish global well posedness for our system by using Bourgain's approach.