  We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with
nonlinear and gain terms and acquire explicit solutions through variable
separation approach. In particular, we deduce some main novel excitations for
the DS equations, and further demonstrate different features of these
excitations. More importantly, the similar solutions and excitations can be
predicted to exist in other related revolution equations such as nonlinear
Schr\"odinger equation to explain the Bose-Einstein condensation.
