
514 CHAPTER 14. RELATED CONCEPTS
harmonic oscillator ground-state mode, the solution is close to a Gaussian shape in
both cases. When f~ deviates from 1, the solution shape is defined by the type of
nonlinearity. For attraction (or - + 1), the shape approaches that of a sech-type soliton,
whereas for repulsion (tr = -1) the solution flattens and is better described by the
Thomas-Fermi approximation.
Figure 14.29 shows the dependence of the invariant Q on the parameter f~ for cr =
4-1, corresponding to two different signs of the scattering length. The dashed curves
show the predictions based on the NLS equation ...