Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited

Egorova, Iryna; Michor, Johanna; Teschl, Gerald

Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited

Authors

Egorova, Iryna

Michor, Johanna

Teschl, Gerald

Description

We investigate soliton solutions of the Toda hierarchy on a quasi-periodic finite-gap background by means of the double commutation method and the inverse scattering transform. In particular, we compute the phase shift caused by a soliton on a quasi-periodic finite-gap background. Furthermore, we consider short range perturbations via scattering theory. We give a full description of the effect of the double commutation method on the scattering data and establish the inverse scattering transform in this setting.
16 pages