Schrödinger system with quintic nonlinearity: spectral stability of multiple sign-changing periodic waves

This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schrödinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral analysis of the associated linearized operators, employing the Floquet theory and comparison theorems. Stability results are derived under periodic perturbations with the same period as the underlying standing waves. Furthermore, we apply the spectral stability theory via Krein signature to determine the spectral stability and instability results.