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

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

MMC.
2023;
Volume 10, Number 4
: pp. 1292–1302
https://doi.org/10.23939/mmc2023.04.1292
Received: September 10, 2021
Revised: December 05, 2023
Accepted: December 05, 2023

Mathematical Modeling and Computing, Vol. 10, No. 4, pp. 1292–1302 (2023)

Authors:
  1. D. S. Kharchenko
  2. V. V. Naradovyi
1
Volodymyr Vynnychenko Central Ukrainian State University
2
Volodymyr Vynnychenko Central Ukrainian State University

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.

wave-packets
modulation stability
gravity waves
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