Ansatz from nonlinear optics applied to trapped Bose-Einstein condensates

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser a laser with self-similar propagation of ultrashort pulses , is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.