Collapse of Solutions of the Nonlinear Schroedinger Equation with a Time-Dependent Nonlinearity: Application to Bose-Einstein Condensates

Journal Article · Fri Jun 24 00:00:00 EDT 2005 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.94.240405· OSTI ID:20696393

Konotop, V V; Pacciani, P ^[1]

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1. Centro de Fisica Teorica e Computacional, Universidade de Lisboa, Av. Prof. Gama Pinto 2, Lisbon 1649-003 (Portugal)

It is proven that periodically varying and sign definite nonlinearity in a general case does not prevent collapse in two-dimensional and three-dimensional nonlinear Schroedinger equations: at any oscillation frequency of the nonlinearity blowing up solutions exist. Contrary to the results known for a sign-alternating nonlinearity, an 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 the existence of collapse is rigorously established. The results are discussed in the context of the mean field theory of Bose-Einstein condensates with time-dependent scattering length.

• OSTI ID: 20696393
• Journal Information: Physical Review Letters, Vol. 94, Issue 24; Other Information: DOI: 10.1103/PhysRevLett.94.240405; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
OSCILLATIONS
PERIODICITY
SCATTERING LENGTHS
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS