  The tachyon field in cosmology is studied by applying the generating function
method to obtain exact solutions. The equation of state parameter of the
tachyon field is $w=-1+\epsilon\dot{\phi^2}$, which can be expressed as a
function in terms of the redshift $z$. Based on these solutions, we propose
some tachyon-inspired dark energy models to explore the properties of the
corresponding cosmological evolution. The explicit relations between Hubble
parameter and redshift enable us to test the models with SNe Ia data sets
easily. In the current work we employ the SNe Ia data with the parameter
$\mathcal{A}$ measured from the SDSS and the shift parameter $\mathcal{R}$ from
WMAP observations to constrain the parameters in our models.
