Article
in Differential Equations and Mathematical Physics, R. Weikard and G. Weinstein (eds.), 375-384, AMS/IP Studies in Advanced Mathematics 16, Amer. Math. Soc., Providence, 2000

On the Initial Value Problem of the Toda and Kac-van Moerbeke Hierarchies

Gerald Teschl

Abstract
We provide a brief review of the initial value problem associated with the Toda and Kac-van Moerbeke hierarchies. We give a simple proof for the basic (global) existence and uniqueness theorem and provide some additional details for the inverse scattering transform. In addition, we also show how to obtain solutions of the Kac-van Moerbeke hierarchy from solutions of the Toda hierarchy via a Miura type transform.

MSC91: Primary 58F07, 34L25; Secondary 39A10, 47B39
Keywords: Toda hierarchy, Kac-van Moerbeke hierarchy, Inverse scattering transform

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