Nonlinear Difference-Differential Equations

Project: Research project

Description

Combining algebro-geometric methods and factorization techniques for finite
difference expressions we provide a complete and self-contained treatment of
all real-valued quasi-periodic finite-gap solutions of both the Toda and
Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the
algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we
employ particular commutation methods in connection with Miura-type
transformations which enable us to transfer whole classes of solutions
(such as finite-gap solutions) from the Toda hierarchy to its modified
counterpart, the Kac-van Moerbeke hierarchy, and vice versa.
StatusFinished
Effective start/end date1/01/9031/01/95