On the Gross–Pitaevskii equation for trapped dipolar quantum gases
- 29 September 2008
- journal article
- research article
- Published by IOP Publishing in Nonlinearity
- Vol. 21 (11) , 2569-2590
- https://doi.org/10.1088/0951-7715/21/11/006
Abstract
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrodinger equation.Keywords
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This publication has 19 references indexed in Scilit:
- Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicityPublished by Elsevier ,2008
- On the Cauchy problem in Sobolev spaces for nonlinear Schrödinger equations with potentialPortugaliae Mathematica, 2008
- On instability for the cubic nonlinear Schrödinger equationComptes Rendus Mathematique, 2007
- LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIALCommunications in Contemporary Mathematics, 2005
- The Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic PotentialSIAM Journal on Mathematical Analysis, 2005
- Semilinear Schrödinger EquationsPublished by American Mathematical Society (AMS) ,2003
- Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensationJournal of Computational Physics, 2003
- Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gasesPhysical Review A, 2002
- High frequency approximation of solutions to critical nonlinear wave equationsAmerican Journal of Mathematics, 1999
- On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equationsJournal of Mathematical Physics, 1977