Solitons and vortices in nonlinear potential wells

Nir Dror*, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrödinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial modulation of the local strength of the self-defocusing nonlinearity. This setting, which may be implemented in optics and Bose-Einstein condensates, aims to extend previous studies, which dealt with single-well nonlinear potentials. In the 1D setting, we find several types of symmetric, asymmetric and antisymmetric states, paying attention to scenarios of the spontaneous symmetry breaking. The single-well model is extended by including rocking motion of the well, which gives rise to Rabi oscillations between fundamental and dipole modes. Analysis of the 2D single-well setting gives rise to stable modes in the form of ordinary dipoles, vortex-antivortex dipoles (VADs), and vortex triangles (VTs), which may be considered as produced by spontaneous breaking of the axial symmetry. The consideration of the DW configuration in 2D reveals diverse types of modes built of components trapped in the two wells, which may be fundamental states and vortices with topological charges m = 1 and 2, as well as VADs (with m = 0) and VTs (with m = 2).

Original languageEnglish
Article number014003
JournalJournal of Optics (United Kingdom)
Issue number1
StatePublished - 30 Nov 2015


  • nonlinear potential wells
  • solitons
  • vortices


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