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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...
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