%0 Journal Article
%T Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
%A F. N. Litvinets
%A A. Yu. Trifonov
%A A. V. Shapovalov
%J Mathematics
%D 2005
%I arXiv
%R 10.1088/0305-4470/39/5/012
%X A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.
%U http://arxiv.org/abs/math-ph/0510054v1