  In this paper, we study the controllable behavior of nonautonomous matter
waves in different "smart" transient trap variations in the context of the
cigar-shaped Bose-Einstein condensates. By utilizing a self-similarity
transformation we reduce the nonautonomous Gross-Pitaevskii (GP) equation to
the elliptic equation that admits soliton solutions. This procedure leads to a
consistency equation which is in the form of Riccati equation. The connection
between the Riccati and the linear Schr\"odinger equation, through the
Cole-Hopf transformation, is exploited profitably here to introduce temporal
trap variations. For our study, we explore the possibility of using one
dimensional exactly solvable (ES) potentials and their newly constructed
rational extensions, as functions of time to introduce interesting temporal
trap modulations. The fact that the regular potentials and their rational
extensions being structurally different, leads to different temporal
modulations. It is exhibited that the soliton behavior with respect to
compression in both these cases is quite different.
