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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...
We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial...
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