Mathematical Research Letters

Volume 13 (2006)

Number 2

Scattering for the Gross-Pitaevskii equation

Pages: 273 – 285

DOI: https://dx.doi.org/10.4310/MRL.2006.v13.n2.a8

Authors

Stephen Gustafson (University of British Columbia)

Kenji Nakanishi (Nagoya University)

Tai-Peng Tsai (University of British Columbia)

Abstract

We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau-Schrödinger) 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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Published 1 January 2006