AbstractBy Whitham's method of averaged Lagrangian two coupled nonlinear Schrödinger equations are derived that give the evolution of the amplitudes of two longitudinal waves, both propagating in the same direction in a hot electron plasma. It is found that a single wave is modulationally stable, while two waves together are modulationally unstable if either the difference between the group velocities of the two waves is sufficiently large, or if this difference is sufficiently small and a coefficient, which couples the two waves, is sufficiently large