On the stability of the dnoidal waves for the Schrödinger-KdV system

We study the periodic Schrödinger-Korteweg de Vries system. We describe the two-parametetric family of $2T$ periodic traveling waves of dnoidal type. The main objective of the paper is to establish their spectral stability with respect to co-periodic perturbations. In the limit $T\to \mathrm{\infty }$, we recover the results of Albert-Angulo, for the stability of the soliton solutions of this system on the real line.