  We put forward a nonlinear wave model describing the fundamental
physio-pathologic features of an aggressive type of brain tumors:
glioblastomas. Our model accounts for the invasion of normal tissue by a
proliferating and propagating rim of active glioma cancer cells in the tumor
boundary and the subsequent formation of a necrotic core. By resorting to
numerical simulations, phase space analysis and exact solutions, we prove that
bright solitary tumor waves develop in such systems.
