Hirota method for the nonlinear Schroedinger equation with an arbitrary linear time-dependent potential

In this paper, a Hirota method is developed for applying to the nonlinear Schroedinger equation with an arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schroedinger equation is decoupled to two equations carefully. With a reasonable assumption the one- and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.