Geodesic
Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System
W. Abou Salem1
1 Department of Mathematics and Statistics, University of Saskatchewan, SK, S7N 5E6, Canada
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 1-12

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The effective dynamics of interacting waves for coupled Schrödinger-Korteweg-de Vries equations over a slowly varying random bottom is rigorously studied. One motivation for studying such a system is better understanding the unidirectional motion of interacting surface and internal waves for a fluid system that is formed of two immiscible layers. It was shown recently by Craig-Guyenne-Sulem [1] that in the regime where the internal wave has a large amplitude and a long wavelength, the dynamics of the surface of the fluid is described by the Schrödinger equation, while that of the internal wave is described by the Korteweg-de Vries equation. The purpose of this letter is to show that in the presence of a slowly varying random bottom, the coupled waves evolve adiabatically over a long time scale. The analysis covers the cases when the surface wave is a stable bound state or a long-lived metastable state.
DOI : 10.1051/mmnp/20127201

W. Abou Salem 1

1 Department of Mathematics and Statistics, University of Saskatchewan, SK, S7N 5E6, Canada 
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W. Abou Salem. Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 1-12. doi: 10.1051/mmnp/20127201

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