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 stringy 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 .