  A dark energy model with a phantom scalar field, an usual scalar field and
the string field theory inspired polynomial potential has been constructed. A
two-parameter set of exact solutions to the Friedmann equations has been found.
We have constructed such string inspired potential that some exact solutions
correspond to the state parameter $w_{DE}>-1$ at large time, whereas other ones
correspond to $w_{DE}<-1$ at large time. We demonstrate that the superpotential
method is very effective to seek new exact solutions. We also present a
two-fields model with a polynomial potential and the state parameter, which
crosses the cosmological barrier infinitely often.
