Modulation stability of wave-packets in a three-layer fluid

This article investigates the modulation stability condition for the problem of wave packet propagation in a three-layer hydrodynamic system "layer with a hard bottom – layer – layer with a lid".  The graphs of the dependence of the modulation stability limits on the thickness of the lower and upper layer and on the density of the middle and upper layers for capillary and gravity waves are illustrated and analyzed.  The evolution equations of the envelope of  wave packets in the form of the second-order nonlinear Schrödinger equation for the lower and upper surfaces of the contact are obtained. The conditions of modulation stability are derived.

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