Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

Details Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

2012-04-13

arxiv.org/abs/1204.3009v1

Physics

Condensed Matter

Quantum Gases

7 pages, 4 figures

Scientific paper

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev\'e transcendent. In each case the potential can be chosen to be time-independent.

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