Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012Solitary waves
|Page(s)||1 - 12|
|Published online||29 February 2012|
Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System
Department of Mathematics and Statistics, University of
Saskatchewan, SK, S7N
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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  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.
Mathematics Subject Classification: 35Q35 / 35Q40 / 35Q51 / 81Q99
Key words: Korteweg-de Vries equation / Schrödinger equation / coupled waves / effective dynamics / adiabatic theorem
© EDP Sciences, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.