Analytical solutions of nonlinear Schrödinger equation with distributed coefficients

We combine the F-expansion method with the homogeneous balance principle to build a strategy to find analytical solitonic and periodic wave solutions to a generalized nonlinear Schrödinger equation with distributed coefficients, linear gain/loss, and nonlinear gain/absorption. In the case of a dimensionless effective Gross-Pitaevskii equation which describes the evolution of the wave function of a quasi-one-dimensional cigar-shaped Bose-Einstein condensate, the building strategy is applied to generate analytical solutions.