New solutions for the quantum drift-diffusion model of semiconductors

In this paper new symmetry reductions and exact solutions are found for the one-dimensional quantum drift–diffusion model for semiconductors based on the Bohm potential. The symmetry reductions are derived by using the nonclassical method developed by Bluman and Cole. Further reductions are obtained by means of other types of symmetry reductions or by ansatz-based reductions. In particular, several types of exact solutions are derived: kinks, k-hump compactons and elliptic traveling waves. The new solutions can display several types of coherent structures.