2007/06/30 by Kevin Rapedius, K. Rapedius, H. J. Korsch · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Strong Light-Matter Interactions #cond-mat.other
paper · pdf · doi:10.1103/physreva.77.063610
published as Phys. Rev. A 77, 063610 (2008) · 9 pages, 6 figures, 1 table
arxiv created 2008/02/13 · openalex publication_date 2008/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The stationary nonlinear Schr"odinger equation (or Gross-Pitaevskii equation) for one-dimensional potential scattering is studied. The nonlinear transmission function shows a distorted profile, which differs from the Lorentzian one found in the linear case. This nonlinear profile function is analyzed and related to Siegert-type complex resonances. It is shown that the characteristic nonlinear profile function can be conveniently described in terms of skeleton functions depending on a few instructive parameters. These skeleton functions also determine the decay behavior of the underlying resonance state. Furthermore, we extend the Siegert method for calculating resonances, which provides a convenient recipe for calculating nonlinear resonances. Applications to a double Gaussian barrier and a square-well potential illustrate our analysis.