On the Toda and Kac–van Moerbeke hierarchies

Mathematische Zeitschrift - Tập 231 - Trang 325-344 - 1999
Gerald Teschl1
1 Institut für Reine und Angewandte Mathematik, RWTH Aachen, D-52056 Aachen, Germany (e-mail: [email protected], URL: http://www.mat.univie.ac.at/~gerald/) , , DE

Tóm tắt

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.