2025/05/01 by Chen Gong, Chen, Gong, Moutinho, Abdon · 1 citation
Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum optics and atomic interactions #Random lasers and scattering media #Spectral Theory (math.SP) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2505.00867
openalex publication_date 2025/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study one-dimensional linear Schrödinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically develop the scattering theory and establish dispersive estimates under the assumption that the potentials move at significantly different velocities, even in the presence of unstable modes. In particular, we prove the existence of wave operators, asymptotic completeness, and pointwise decay of solutions, without requiring the absence of threshold resonances. Our analysis set up the fundamental work for studying the nonlinear dynamics of multi-solitons, including asymptotic stability and collisions.