Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation

We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech²? type time-varying quadratic trapping potential for two different choices of linear potential.