Scattering Theory and dispersive estimates for general $1$d Charge Transfer Models

We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the construction of distorted Fourier transforms adapted to the multi-potential framework, we remove the large-velocity separation assumption imposed in [8]. This work thus completes the full scattering theory and dispersive analysis for general one-dimensional charge transfer models. These dispersive estimates provide the foundation for analyzing asymptotic stability and collision phenomena for multi-solitons in a general setting.