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.
|Number of pages||7|
|Journal||Communications in Nonlinear Science & Numerical Simulation|
|Early online date||15 Mar 2010|
|Publication status||Published - Jan 2011|
- nonlinear Schrodinger equation
- Bose–Einstein condensate (BEC)
- Hirota bilinear method