Article
Math. Z. 231, 325-344 (1999) [DOI: 10.1007/PL00004732]

On the Toda and Kac-van Moerbeke Hierarchies

Gerald Teschl

Abstract
We provide a comprehensive treatment of the single and double commutation method as a tool for constructing soliton solutions of the Toda and Kac-van Moerbeke hierarchy on arbitrary background. In addition, we present a novel construction based on the single commutation method. As an illustration we compute the N-soliton solution of the Toda and Kac-van Moerbeke hierarchy.

MSC91: Primary 58F07, 58F37; Secondary 39A10, 47B39
Keywords: Toda hierarchy, Kac-van Moerbeke hierarchy, commutation method

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