Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited
arXiv:nlin/0609016 · doi:10.1002/mana.200610752
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.
arXiv comment16 pages
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Cited by in corpus (6)
- Long-Time Asymptotics for the Toda Lattice in the Soliton Region
- Stability of the periodic Toda lattice under short range perturbations
- Stability of the Periodic Toda Lattice in the Soliton Region
- Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
- Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data
- Stability of the Periodic Toda Lattice: Higher Order Asymptotics