  Trapped Bose atoms cooled down to temperatures below the Bose-Einstein
condensation temperature are considered. Stationary solutions to the
Gross-Pitaevskii equation (GPE) define the topological coherent modes,
representing nonground-state Bose-Einstein condensates. These modes can be
generated by means of alternating fields whose frequencies are in resonance
with the transition frequencies between two collective energy levels
corresponding to two different topological modes. The theory of resonant
generation of these modes is generalized in several aspects: Multiple-mode
formation is described; a shape-conservation criterion is derived, imposing
restrictions on the admissible spatial dependence of resonant fields; evolution
equations for the case of three coherent modes are investigated; the complete
stability analysis is accomplished; the effects of harmonic generation and
parametric conversion for the topological coherent modes are predicted. All
considerations are realized both by employing approximate analytical methods as
well as by numerically solving the GPE. Numerical solutions confirm all
conclusions following from analytical methods.
