  We present a large family of {\it{exact}} solitary wave solutions of the one
dimensional Gross-Pitaevskii equation, with time-varying scattering length and
gain/loss, in both expulsive and regular parabolic confinement regimes. The
consistency condition governing the soliton profiles is shown to map on to a
{\it{linear}} Schr\"odinger eigenvalue problem, thereby enabling one to find
analytically the effect of a wide variety of temporal variations in the control
parameters, which are experimentally realizable. Corresponding to each solvable
quantum mechanical system, one can identify a soliton configuration. These
include soliton trains in close analogy to experimental observations of
Strecker {\it{et al.,}} [Nature {\bf{{417}}{150}{2002}], spatio-temporal
dynamics, solitons undergoing rapid amplification, collapse and revival of
condensates and analytical expression of two-soliton bound states, to name a
few.
