Mathematical Research Letters

Volume 13, Issue 2, March 2006 pp. 273-285.

Scattering for the Gross-Pitaevskii equation

Authors: Stephen Gustafson (1), Kenji Nakanishi (2), and Tai-Peng Tsai (3)
Author institution: University of British Columbia (1), Nagoya University (2), and University of British Columbia (3)

Summary: We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau-Schr\"odinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces.

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