Scattering for the Gross-Pitaevskii equation

Details Scattering for the Gross-Pitaevskii equation Scattering for the Gross-Pitaevskii equation

2005-10-04

arxiv.org/abs/math/0510080v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We investigate the asymptotic behavior at time infinity of solutions close to
a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau
Schroedinger) 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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