Long-wave short-wave resonance case for a generalized Davey–Stewartson system

It is observed that the generalized Davey–Stewartson equations are not valid for a long-wave short-wave resonance case. In the case where the phase velocity of the long longitudinal wave is equal to the group velocity of the short transverse wave, new (2+1)(2+1) dimensional evolution equations, called the long-wave short-wave interaction equations, are derived to describe the resonance case. The special solutions of the long-wave short-wave interaction equations are also obtained in terms of Jacobian elliptic functions.