Spectrum of Coherent Modes for Trapped Bose Gas
  The spectrum of coherent modes for dilute atomic Bose gas, confined in a cylindrical trap, is calculated by applying optimized perturbation theory and the technique of self-similar root approximants. The latter technique makes it possible to derive accurate analytical formulas. The obtained expressions are valid for arbitrary energy levels of all excited nonlinear coherent modes and for different traps, spherical, sigar-shape, and disk-shape. 
V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato