Dispersive analysis of charge transfer models

Abstract

Abstract We prove dispersive estimates for the time‐dependent Schrödinger equation with a charge transfer Hamiltonian. As a by‐product we also obtain another proof of asymptotic completeness of the wave operators for a charge transfer model established earlier by K. Yajima and J. M. Graf. We also consider a more general matrix non‐self‐adjoint charge transfer problem. This model appears naturally in the study of nonlinear multisoliton systems and is specifically motivated by the problem of asymptotic stability of multisoliton states of a nonlinear Schrödinger equation. © 2004 Wiley Periodicals, Inc.