On the Gross-Pitaevskii equation for trapped dipolar quantum gases

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.

21 pages

References in corpus (2)

• Dipolar Bose-Einstein condensates with dipole-dependent scattering length
• Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

Cited by in corpus (6)

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• On the mass transfer in the 3D Pitaevskii model
• Small-data global existence of solutions for the Pitaevskii model of superfluidity
• An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation