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It is universally accepted that the cubic, nonlinear Schrodinger equation(NLS) models the dynamics of narrow-bandwidth wave packets consisting of shortdispersive waves, while the Kortewegde Vries equation (KdV) models thepropagation of long waves in dispersive media. A system that couples the twoequations seems attractive to model the interaction of long and short waves andsuch a system has been studied over the last few decades. However, questionsabout the validity of the system in the study of water waves were raised in ourprevious work where we presented our analysis using the fifth-order KdV as thestarting point. In this paper, these questions are settled unequivocally as weshow that the NLS-KdV system or even the linear Schrodinger-KdV system cannotbe resulted from the full Euler equations formulated in the study of waterwaves.

On the (in)validity of the NLS-KdV system in the study of water waves