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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics