  Gaussian distribution is commonly used as a good approximation to study the
trapped one-component Bose-condensed atoms with relatively small nonlinear
effect. It is not adequate in dealing with the one-component system of large
nonlinear effect, nor the two-component system where phase separation exists.
We propose a modified Gaussian distribution which is more effective when
dealing with the one-component system with relatively large nonlinear terms as
well as the two-component system. The modified Gaussian is also used to study
the breathing modes of the two-component system, which shows a drastic change
in the mode dispersion at the occurrence of the phase separation. The results
obtained are in agreement with other numerical results.
