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

Abstract

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

References in corpus (4)

• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Stability of Periodic Soliton Equations under Short Range Perturbations
• Algebro-Geometric Constraints on Solitons with Respect to Quasi-Periodic Backgrounds
• Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

Cited by in corpus (1)

• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds