Exact solutions and excitations for the Davey-Stewartson equations with nonlinear and gain terms

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.