Remarks on nonlinear Schroedinger equations with harmonic potential

Details Remarks on nonlinear Schroedinger equations with harmonic potential Remarks on nonlinear Schroedinger equations with harmonic potential

2001-11-24

arxiv.org/abs/cond-mat/0111469v5

Annales Henri Poincare, vol. 3, no.4 (2002), 757-772.

Physics

Condensed Matter

16 pages, no figure

Scientific paper

Bose-Einstein condensation is usually modeled by nonlinear Schroedinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schroedinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the blow up time.

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