Solitary waves and atomic population transfer via the continuum

Exact analytic results are presented that represent a pair of solitary waves that can propagate through an atomic medium with their shapes invariant while producing transfer of atoms or molecules from one bound state to another via a continuum. The speed of the waves and the amount of population transfer are given in terms of the wave amplitudes. A general (not solitary wave) solution for the case of a single wave is presented, together with a nonlinear Beer’s law of absorption.