Nonlinear Interaction of Dispersive Waves with Equal Group Velocity

A new type of wave-wave interaction is presented, which is excited between pairs of waves with equal group velocity. A simple model in nonlinear optics is considered as a concrete example of dispersive medium. By using the multiple scale method, the slow modulation of the complex envelopes is described by simultaneous nonlinear Schrodinger equations. It is then shown that a stable plane wave with constant amplitude tends to become modulationally unstable owing to the existence of another wave with the same group velocity. Some exact solutions are found for this system of equations.