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.
|Original language||English (US)|
|Number of pages||68|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Feb 2005|
All Science Journal Classification (ASJC) codes
- Applied Mathematics