On collapse in the nonlinear Schrodinger equation with time dependent nonlinearity. Application to Bose-Einstein condensates

Abstract

It is proven that periodically varying and sign definite nonlinearity in a general case does not prevent collapse in two- and three-dimensional nonlinear Schrodinger equations: at any oscillation frequency of the nonlinearity blowing up solutions exist. Contrary to the results known for a sign alternating nonlinearity, increase of the frequency of oscillations accelerates collapse. The effect is discussed from the viewpoint of scaling arguments. For the three-dimensional case a sufficient condition for existence of collapse is rigorously established. The results are discussed in the context of the meanfield theory of Bose-Einstein condensates with time dependent scattering length.

5 pages, 1 figure, talk given at IMACS Conference on Nonlinear Evolution Equations and Wave Phenomena. Athens, Georgia, USA, April 11-14, 2005

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