Conservation laws and solutions of a quantum drift-diffusion model for semiconductors

• Non-linear self-adjointness of a model of quantum semiconductors is proved.
• Infinite set of conservation laws of the model is constructed.
• Conservation form of the quantum drift-diffusion model is found.
• Exact solutions provided by the method of conservation laws are considered.

A non-linear system of partial differential equations describing a quantum drift-diffusion model for semiconductor devices is investigated by methods of group analysis. An infinite number of conservation laws associated with symmetries of the model are found. These conservation laws are used for representing the system of equations under consideration in the conservation form. Exact solutions provided by the method of conservation laws are discussed. These solutions are different from invariant solutions.