We construct cosmological models with two scalar fields, which has the
structure as in the ghost condensation model or k-essence model. The models can
describe the stable phantom crossing, which should be contrasted with one
scalar tensor models, where the infinite instability occurs at the crossing the
phantom divide. We give a general formulation of the reconstruction in terms of
the e-foldings N by including the matter although in the previous two scalar
models, which are extensions of the scalar tensor model, it was difficult to
give a formulation of the reconstruction when we include matters. In the
formulation of the reconstruction, we start with a model with some arbitrary
functions, and find the functions which generates the history in the expansion
of the universe. We also give general arguments for the stabilities of the
models and the reconstructed solution. The viability of a model is also
investigated by comparing the observational data.Comment: 12 pages, 1 figur
