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Modulated amplitude waves with nonzero phases in Bose-Einstein condensates. (English) Zbl 1272.82025
Summary: In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using the averaging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and obtain that all these modulated amplitude waves (periodic or quasi-periodic) form a foliation by varying the integration constant continuously. Compared with the previous work, modulated amplitude waves studied in this paper have nontrivial phases and this makes the problem become more difficult, since it involves some singularities. {\par© 2011 American Institute of Physics}

MSC:
82C22Interacting particle systems
35Q55NLS-like (nonlinear Schrödinger) equations
35B10Periodic solutions of PDE
35B15Almost and pseudo-almost periodic solutions of PDE
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