Remarks on the nonlinear Schroedinger equation with harmonic potential

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  • 24 November 2001
Abstract
We solve the local Cauchy problem for the nonlinear Schroedinger equation with harmonic potential, an equation appearing in the study of Bose-Einstein condensation. We prove that the mathematical study of this equation is very close to the study of the same equation without potential, thanks to two explicit operators. We prove the analogue of the pseudo-conformal conservation law, and results for the global Cauchy problem or wave collapse.

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