Stability of the periodic traveling waves of the Boussinesq and symmetric regularized long-wave equations

Abstract Our particular interest is in the periodic traveling waves, which we construct and study in detail. The question of the spectral stability of spatially periodic waves for the Boussinesq and symmetric regularized long-wave equations with fifth-order nonlinearity are studied. The simultaneous consideration of the two equations is justified, because they have many similarities. However, they have certain differences as well. The main result of this paper is a theorem which establishes spectral stability (instability) of the found periodic waves for the studied equations.