Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System

W. Abou Salem
2012 Mathematical Modelling of Natural Phenomena  
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
more » ... ngth, 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 fatcat:7aj244ougjbxvnldmx4d3tsyou