2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222852We 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 pagesExactly Solvable and Integrable SystemsMathematical Physicstext