  We present a series of chirp-free and chirped analytical nonautonomous
soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with
distributed coefficients by Darboux transformation from a trivial seed. For
chirpfree nonautonomous soliton, the dispersion management term can change the
motion of nonautonomous soliton and do not affect its shape at all.
Especially,the classical optical soliton can be presented with variable
dispersion term and nonlinearity when there is no gain. For chirped
nonautonomous soliton, dispersion management can affect the shape and motion of
nonautonomous solitons meanwhile. The periodic dispersion term can be used to
control its "breathing" shape, and it does not affect the trajectory of
nonautonomous soliton center with a certain condition.
