Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

R. A. Kraenkel, Nakkeeran Kaliyaperumal, K. W. Chow

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We investigate the nonlinear Schrödinger equation with a time-dependent nonlinear coefficient. By means of Painlevé analysis we establish the integrability for a particular form of the nonlinear coefficient. The corresponding soliton solution is shown to be of the self-similar kind. We discuss the implications of the result to the dynamics of attractive Bose-Einstein condensates under Feshbach-managed nonlinearity and explore the possibility of a managed self-similar evolution in 1D condensates.

Original languageEnglish
Pages (from-to)86-92
Number of pages7
JournalCommunications in Nonlinear Science & Numerical Simulation
Issue number1
Early online date15 Mar 2010
Publication statusPublished - Jan 2011



  • nonlinear Schrodinger equation
  • Bose–Einstein condensate (BEC)
  • Soliton
  • Hirota bilinear method

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