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.
Hioe, Foek T. and Carroll, C. E. (1997). "Solitary waves and atomic population transfer via the continuum." Physical Review A 56.3, 2292-2298.
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©1997, The American Physical Society. Original publication is available at http://link.aps.org/doi/10.1103/PhysRevA.56.2292