Hakkaev, Sevdzhan2024-06-122024-06-1220240022-247X1096-0813https://doi.org/10.1016/j.jmaa.2023.128016https://hdl.handle.net/20.500.14551/23102The nonlinear dispersive system is considered in the periodic context. The main goal of the paper is to study spectral stability of periodic traveling waves. We show that under certain conditions of the parameters the cnoidal waves are spectrally stable/unstable and dnoidal waves are spectrally stable for all values of the parameters. The proof relies on an instability index count theory for Hamiltonian system developed in [19]. 2023 Elsevier Inc. All rights reserved.en10.1016/j.jmaa.2023.128016info:eu-repo/semantics/closedAccessPeriodic Traveling WavesSpectral StabilityNonlinear Wave EquationNonlinear Dispersive MediaAmplitude Long WavesBoussinesq EquationsTraveling-WavesSystemsEigenvaluesArticle5331N/AWOS:0011598244000012-s2.0-85180423614Q1