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Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions. (English) Zbl 1375.35485
Summary: We study asymptotic behaviour at time infinity of solutions close to the non-zero constant equilibrium for the Gross-Pitaevskii equation in two and three spatial dimensions. We construct a class of global solutions with prescribed dispersive asymptotic behavior, which is given in terms of the linearized evolution.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
76A25 Superfluids (classical aspects)
82D50 Statistical mechanics of superfluids
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