Exact soliton-like solutions of the radial Gross–Pitaevskii equation

2012/04/30 by Lauri Toikka, L A Toikka, Jarmo Hietarinta +3
Physics and Astronomy · #Dynamics (music) #Exact differential equation #Exact solutions in general relativity #Matrix similarity #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Phase (matter) #Quantum Mechanics and Non-Hermitian Physics #Ring (chemistry) #Similarity solution #Transformation (genetics) #cond-mat.quant-gas #nlin.SI

paper · pdf · doi:10.1088/1751-8113/45/48/485203

published as J. Phys. A: Math. Theor. 45 (2012) 485203 · 8 pages, 7 figures. Version 2: stability analysis of the dark solution

arxiv created 2012/06/08 · openalex publication_date 2012/11/19 · arxiv updated 2012/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

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 Painlevé transcendent. In each case the potential can be chosen to be time independent.

Citations

• Ring dark solitons
• Time-averaged adiabatic ring potential for ultracold atoms
• Tailoring of motional states in double-well potentials by time-dependent processes
• Smooth inductively coupled ring trap for atoms
• Ring Dark Solitons and Vortex Necklaces in Bose-Einstein Condensates
• Oblique Dark Solitons in Supersonic Flow of a Bose-Einstein Condensate