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Scattering for the Gross-Pitaevskii equation

S. Gustafson·K. Nakanishi·T. -P. Tsai
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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 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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S. Gustafson, K. Nakanishi, T. -P. Tsai. 2005-10-04. Scattering for the Gross-Pitaevskii equation. https://arxiv.org/abs/math/0510080

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