Simulation of a Coupled System of Long Wave-Short Waves With a Slight Detuning in Group Velocities

The resonances among long and short waves have been studied intensively. The focus of this paper is on flow configurations with two short wave groups with slight detuning in group velocities. This detuning effect will introduce a much richer set of dynamics as the mismatch in group velocities will have profound effects on the motion of pulses. Exact solitary waves are calculated for the coupled set of nonlinear evolution equations by the Hirota bilinear transform. The Hopscotch method is applied to solve the set of equations numerically. Physically, the goal is to study the effects of mismatch in group velocities and the initial phase difference of arbitrary solitary pulses between wave guides. The outcome will depend on the strength of the group velocity differences, initial amplitudes and phase differences.